The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (Q4605404)

scientific article; zbMATH DE number 6842163

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English	The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion	scientific article; zbMATH DE number 6842163

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instance of

scholarly article

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title

The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (English)

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zbMATH Open document ID

1492.35151

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DOI

10.1007/978-3-319-61494-6_5

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author

Juan Luis Vazquez

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published in

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

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publication date

22 February 2018

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full work available at URL

https://arxiv.org/abs/1706.08241

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Mathematics Subject Classification ID

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MaRDI publication profile

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Continuous Dependence Estimates for Nonlinear Fractional Convection-diffusion Equations

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Porous medium flow with both a fractional potential pressure and fractional time derivative

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Well-posedness of a fractional porous medium equation on an evolving surface

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A gradient flow approach to an evolution problem arising in superconductivity

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Q5441008

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Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices

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Q3162662

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Parabolic quasilinear equations minimizing linear growth functionals

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The focusing problem for the radially symmetric porous medium equation

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Lévy Processes and Stochastic Calculus

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ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS

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Q3030503

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Q4180668

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Local behavior of solutions of quasilinear parabolic equations

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Anomalous exponents in nonlinear diffusion

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Q4089232

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Multidimensional nonlinear diffusion arising in population genetics

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Interfaces with a corner point in one-dimensional porous medium flow

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Limit behaviour of focusing solutions to nonlinear diffusions

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Continuity of the temperature in boundary heat control problems

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The Fisher-KPP problem with doubly nonlinear ``fast'' diffusion

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Q3920841

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A Widder's type theorem for the heat equation with nonlocal diffusion

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Diffusions and Elliptic Operators

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Q4073824

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Q4888858

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AGGREGATION AND SPREADING VIA THE NEWTONIAN POTENTIAL: THE DYNAMICS OF PATCH SOLUTIONS

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Two‐dimensional chemotaxis models with fractional diffusion

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Nonlinear diffusion of dislocation density and self-similar solutions

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Barenblatt profiles for a nonlocal porous medium equation

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The nonlocal porous medium equation: Barenblatt profiles and other weak solutions

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Non-local gradient dependent operators

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Asymptotics of the fast diffusion equation via entropy estimates

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Some Theorems on Stable Processes

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Censored stable processes

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Total variation flow and sign fast diffusion in one dimension

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Asymptotics of the porous media equation via Sobolev inequalities

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Global positivity estimates and Harnack inequalities for the fast diffusion equation

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Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations

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Quantitative local and global a priori estimates for fractional nonlinear diffusion equations

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A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains

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Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds.

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Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

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Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold

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Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains

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Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations

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Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains

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Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains

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Optimal existence and uniqueness theory for the fractional heat equation

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The one-dimensional Keller–Segel model with fractional diffusion of cells

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Nonlocal heat equations: regularizing effect, decay estimates and Nash inequalities

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Viscosity solutions for quasilinear degenerate parabolic equations of porous medium type

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A concave—convex elliptic problem involving the fractional Laplacian

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Nonlocal diffusion and applications

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Q4855688

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Front propagation in Fisher-KPP equations with fractional diffusion

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The influence of fractional diffusion in Fisher-KPP equations

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Positive solutions of nonlinear problems involving the square root of the Laplacian

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Q4447215

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Non-local Diffusions, Drifts and Games

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Continuity of the Density of a Gas Flow in a Porous Medium

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Q5462452

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An Extension Problem Related to the Fractional Laplacian

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Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

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Nonlinear porous medium flow with fractional potential pressure

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Asymptotic behaviour of a porous medium equation with fractional diffusion

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C1,α regularity of the free boundary for the n-dimensional porous media equation

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Q3786839

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Regularity theory for parabolic nonlinear integral operators

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Regularity of solutions of the fractional porous medium flow

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The Geometry of Diffusing and Self-Attracting Particles in a One-Dimensional Fair-Competition Regime

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Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity

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Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

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Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure

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Global existence, singularities and ill-posedness for a nonlocal flux

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Incompressible flow in porous media with fractional diffusion

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Fractional Laplacian in conformal geometry

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Regularity for solutions of nonlocal parabolic equations. II

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Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities

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Two-sided eigenvalue estimates for subordinate processes in domains

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Heat kernel estimates for the Dirichlet fractional Laplacian

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Two-sided heat kernel estimates for censored stable-like processes

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Q3413423

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Entropy solution theory for fractional degenerate convection-diffusion equations

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Financial Modelling with Jump Processes

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Regularity Theory for Local and Nonlocal Minimal Surfaces: An Overview

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Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces

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Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations

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Q3236921

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Q3766152

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Discretizations of the Spectral Fractional Laplacian on General Domains with Dirichlet, Neumann, and Robin Boundary Conditions

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Degenerate diffusions. Initial value problems and local regularity theory

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Weak and smooth solutions for a fractional Yamabe flow: The case of general compact and locally conformally flat manifolds

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Heat Kernel Bounds for Second Order Elliptic Operators on Riemannian Manifolds

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Q3252874

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Travelling wave behaviour for a Porous-Fisher equation

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Travelling waves and finite propagation in a reaction-diffusion equation

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A fractional porous medium equation

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A General Fractional Porous Medium Equation

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Classical solutions for a logarithmic fractional diffusion equation

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Nonlocal filtration equations with rough kernels

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Bubbling Blow-Up in Critical Parabolic Problems

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Finite difference method for a fractional porous medium equation

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Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type

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Q3726641

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Degenerate parabolic equations

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Harnack's Inequality for Degenerate and Singular Parabolic Equations

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Hitchhiker's guide to the fractional Sobolev spaces

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A simple mathematical model inspired by the Purkinje cells: from delayed travelling waves to fractional diffusion

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An Error Estimate for a Finite-element Approximation of an Elliptic Variational Inequality Formulation of a Hele—Shaw Moving-boundary Problem

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The fractional Keller–Segel model

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Q4399897

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Q3057566

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Q2871888

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The local regularity of solutions of degenerate elliptic equations

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Solutions fortes et comportement asymptotique pour un modèle de convection naturelle en milieu poreux. (Strong solutions and asymptotic behaviour for a natural convection problem in porous media)

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Local Regularity for Parabolic Nonlocal Operators

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The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium

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Q5547841

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Continuation of blowup solutions of nonlinear heat equations in several space dimensions

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The problem of blow-up in nonlinear parabolic equations

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Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits

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Macroscopic evolution of particle systems with short- and long-range interactions

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Q4061759

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Elliptic partial differential equations of second order

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Nonlocal Operators with Applications to Image Processing

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Recent Progress on the Fractional Laplacian in Conformal Geometry

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Fractional conformal Laplacians and fractional Yamabe problems

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Fundamental solution of the heat equation on an arbitrary Riemannian manifold

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Q5484092

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Radial fast diffusion on the hyperbolic space

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Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincaré inequalities

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Fractional porous media equations: existence and uniqueness of weak solutions with measure data

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The porous medium equation with large initial data on negatively curved Riemannian manifolds

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Reflected symmetric \(\alpha\)-stable processes and regional fractional Laplacian

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On the diffusion of biological populations

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Q3812872

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Q4398321

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Complex variable methods in Hele–Shaw moving boundary problems

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Explicit Barenblatt profiles for fractional porous medium equations

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Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution

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Radial equivalence for the two basic nonlinear degenerate diffusion equations

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Nonequilibrium scaling limit for a tagged particle in the simple exclusion process with long jumps

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Limit theorems for additive functionals of a Markov chain

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Nonequilibrium fluctuations for a tagged particle in mean-zero one-dimensional zero-range processes

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A fractional Yamabe flow and some applications

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Q3284846

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Propagation of thermal waves in an inhomogeneous medium

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Fundamental solutions and asymptotic behaviour for the p-Laplacian equations

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Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density

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On the growth of solutions of quasi‐linear parabolic equations

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A priori estimates for integro-differential operators with measurable kernels

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Flatness implies smoothness for solutions of the porous medium equation

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Hölder estimates for singular non-local parabolic equations

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Q3905599

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On the Fisher–KPP equation with fast nonlinear diffusion

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Q4865742

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Global well-posedness for the critical 2D dissipative quasi-geostrophic equation

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Blow up and regularity for fractal Burgers equation

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Q5601102

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Linear and quasilinear elliptic equations

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Q5562267

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Q5666837

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The Role of Critical Exponents in Blowup Theorems

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Exploding solutions for a nonlocal quadratic evolution problem

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Q4354424

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On the hydrodynamic limit of Ginzburg-Landau vortices.

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Q5549989

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A gradient flow approach to the porous medium equation with fractional pressure

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Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds

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A two-dimensional model for quasigeostrophic flow: Comparison with the two-dimensional Euler flow

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Fractional \(p\)-Laplacian evolution equations

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The Stefan problem. Translated from the Russian by Marek Niezgódka and Anna Crowley

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Fractional diffusion limit for collisional kinetic equations

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The random walk's guide to anomalous diffusion: A fractional dynamics approach

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Q5757489

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A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations

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A harnack inequality for parabolic differential equations

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On Fractional Laplacians

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PARABOLIC EQUATIONS

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Continuity of Solutions of Parabolic and Elliptic Equations

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A PDE approach to fractional diffusion in general domains: a priori error analysis

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A PDE Approach to Space-Time Fractional Parabolic Problems

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Extension properties and boundary estimates for a fractional heat operator

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Q3269387

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The Fractional Laplacian

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On the Evolutionary Fractional<i>p</i>-Laplacian

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Long time behavior for the inhomogeneous PME in a medium with slowly decaying density

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Some Hele Shaw flows with time-dependent free boundaries

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Obstructions to existence in fast-diffusion equations

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The Dirichlet problem for the fractional Laplacian: regularity up to the boundary

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Q5624097

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The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid

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Partial Differential Equations in Action

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Regularity for parabolic integro-differential equations with very irregular kernels

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Long-time asymptotics for the porous medium equation: the spectrum of the linearized operator

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A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators

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Local behavior of solutions of quasi-linear equations

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On the spectrum of two different fractional operators

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Holder estimates for solutions of integro differential equations like the fractional laplace

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Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application

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Q5188501

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Asymptotic behaviour of the doubly nonlinear diffusion equation \(u_t=\Delta_pu^m\) on bounded domains

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The Fisher-KPP Equation with Nonlinear Fractional Diffusion

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Finite and infinite speed of propagation for porous medium equations with fractional pressure

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Transformations of self-similar solutions for porous medium equations of fractional type

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Finite and infinite speed of propagation for porous medium equations with nonlocal pressure

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Existence of weak solutions for a general porous medium equation with nonlocal pressure

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Q5607484

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Extension Problem and Harnack's Inequality for Some Fractional Operators

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Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation

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The chemical basis of morphogenesis

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From the long jump random walk to the fractional Laplacian

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Lectures on diffusion problems and partial differential equations. Notes by Pl. Muthuramalingam, Tara R. Nanda

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Brownian motion and random walks on manifolds

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Nonexistence of solutions for nonlinear heat equations of fast-diffusion type

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Asymptotic behaviour for the porous medium equation posed in the whole space.

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The Dirichlet problem for the porous medium equation in bounded domains. Asymptotic behavior

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Nonlinear Diffusion with Fractional Laplacian Operators

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Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators

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Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type

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The mesa problem for the fractional porous medium equation

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Fundamental solution and long time behavior of the porous medium equation in hyperbolic space

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The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation

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Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D

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Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type

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Optimal estimates for fractional fast diffusion equations

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Classical solutions and higher regularity for nonlinear fractional diffusion equations

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The Mathematics of Financial Derivatives

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On the heat kernel of a complete Riemannian manifold

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