Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
From MaRDI portal
Publication:2445380
DOI10.1016/j.aim.2013.09.018zbMath1288.35127arXiv1210.2594OpenAlexW2026667565MaRDI QIDQ2445380
Matteo Bonforte, Juan Luis Vazquez
Publication date: 14 April 2014
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1210.2594
fractional Laplacianfast diffusioninitial traceslow diffusionvery fast diffusionexistence for large datapositivity estimatesweighted global estimates
Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45) Fractional partial differential equations (35R11)
Related Items
Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application, Classical solutions and higher regularity for nonlinear fractional diffusion equations, Existence of entropy solutions for nonsymmetric fractional systems, Existence and uniqueness of an attractive nonlinear diffusion system, Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations, Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations, The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation, The fractional Laplacian in power-weighted \(L^{p}\) spaces: integration-by-parts formulas and self-adjointness, Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type, A Liouville theorem for a class of reaction-diffusion systems with fractional diffusion, Strong Competition versus Fractional Diffusion: The Case of Lotka-Volterra Interaction, Gradient estimates and symmetrization for Fisher-KPP front propagation with fractional diffusion, Exponential propagation for fractional reaction-diffusion cooperative systems with fast decaying initial conditions, Fractional porous media equations: existence and uniqueness of weak solutions with measure data, Finite and infinite speed of propagation for porous medium equations with nonlocal pressure, Existence and multiplicity results for nonlocal Lane-Emden systems, Blow‐up results for a semi‐linear structural damped wave model with nonlinear memory, Unnamed Item, Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, Some free boundary problems involving non-local diffusion and aggregation, Initial trace of positive solutions to fractional diffusion equations with absorption, On nonexistence of solutions to some time space fractional evolution equations with transformed space argument, Semilinear nonlocal elliptic equations with source term and measure data, Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains, Solvability of the fractional hyperbolic Keller-Segel system, Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations, Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds., The Cauchy-Dirichlet problem for singular nonlocal diffusions on bounded domains, The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour, Solution blow-up for a fractional fourth-order equation of Moore-Gibson-Thompson type with nonlinearity nonlocal in time, Stability of the separable solutions for a nonlinear boundary diffusion problem, The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion, The fractional porous medium equation on the hyperbolic space, Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators, On the Cauchy problem for a general fractional porous medium equation with variable density, Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type, A dynamically consistent method to solve nonlinear multidimensional advection-reaction equations with fractional diffusion, Porous medium equation with nonlocal pressure in a bounded domain, Entropy solutions of doubly nonlinear fractional Laplace equations, Optimal estimates for fractional fast diffusion equations, A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains, Existence of weak solutions for a general porous medium equation with nonlocal pressure, Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range, Spectrum of the fractional \(p\)-Laplacian in \(\mathbb{R}^N\) and decay estimate for positive solutions of a Schrödinger equation, Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos, Optimal existence and uniqueness theory for the fractional heat equation, Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D, Representation of solutions and large-time behavior for fully nonlocal diffusion equations, Asymptotics of chemotaxis systems with fractional dissipation for small data in critical Sobolev space, Study of the existence of supersolutions for nonlocal equations with gradient terms, Uniqueness of entropy solutions to fractional conservation laws with ``Fully infinite speed of propagation, The fractional Laplacian has infinite dimension, Backward estimates for nonnegative solutions to a class of singular parabolic equations, The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case, Uniqueness of very weak solutions for a fractional filtration equation, Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains, Well-posedness of semilinear strongly damped wave equations with fractional diffusion operators and \(C^0\) potentials on arbitrary bounded domains, Harnack's inequality for parabolic nonlocal equations, Energy and large time estimates for nonlinear porous medium flow with nonlocal pressure in \(\mathbb{R}^N\), Explicit Barenblatt profiles for fractional porous medium equations, On existence and regularity of a terminal value problem for the time fractional diffusion equation, Harnack inequality and self-similar solutions for fully nonlinear fractional parabolic equations, Nonlocal equations with measure data, Transformations of self-similar solutions for porous medium equations of fractional type, Harnack estimates at large: sharp pointwise estimates for nonnegative solutions to a class of singular parabolic equations, On multi-singular integral equations involving n weakly singular kernels, Existence of Neumann and singular solutions of the fast diffusion equation, Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains, On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Entropy solution theory for fractional degenerate convection-diffusion equations
- A fractional porous medium equation
- Nonlinear diffusion of dislocation density and self-similar solutions
- Degenerate parabolic equations
- Nonlinear porous medium flow with fractional potential pressure
- Nonequilibrium fluctuations for a tagged particle in mean-zero one-dimensional zero-range processes
- Global positivity estimates and Harnack inequalities for the fast diffusion equation
- Non-negative solutions to fast diffusions
- Continuity of the temperature in boundary heat control problems
- Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations
- Limit theorems for additive functionals of a Markov chain
- Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities
- Asymptotic behaviour of a porous medium equation with fractional diffusion
- Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations
- A General Fractional Porous Medium Equation
- Nonlinear Diffusion with Fractional Laplacian Operators
- Harnack's Inequality for Degenerate and Singular Parabolic Equations
- The Initial Trace of a Solution of the Porous Medium Equation
- Lévy Processes and Stochastic Calculus
- The Cauchy Problem for u t = Δu m When 0 < m < 1
- Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
- Financial Modelling with Jump Processes
- An Extension Problem Related to the Fractional Laplacian
- Nonequilibrium scaling limit for a tagged particle in the simple exclusion process with long jumps
- The random walk's guide to anomalous diffusion: A fractional dynamics approach