scientific article; zbMATH DE number 5058450

Publication date: 28 September 2006

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

fast diffusion equation symmetrization nonlinear parabolic equations extinction nonlinear semigroups scaling porous medium equation decay of solutions smoothing effect Marcinkiewicz spaces \(p\)-Laplacian equation concentration doubly nonlinear equation nonlinearities of power type

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items

Bounded weak and strong time periodic solutions to a three-dimensional chemotaxis-Stokes model with porous medium diffusion, On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient, The Continuous Formulation of Shallow Neural Networks as Wasserstein-Type Gradient Flows, Local approximation of heterogeneous porous medium equation by some nonlocal dispersal problems, Degenerate and Singular Porous Medium Type Equations with Measure Data, Solutions with snaking singularities for the fast diffusion equation, Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations, From the highly compressible Navier-Stokes equations to fast diffusion and porous media equations, existence of global weak solution for the quasi-solutions, Stability of non-isolated asymptotic profiles for fast diffusion, Kaplan's penalty operator in approximation of a diffusion-absorption problem with a one-sided constraint, The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation, Some properties of the Yamabe soliton and the related nonlinear elliptic equation, Local-in-time regularity results for some flux-limited diffusion equations of porous media type, Singular-Degenerate Multivalued Stochastic Fast Diffusion Equations, Exact decay rate of a nonlinear elliptic equation related to the Yamabe flow, A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving, Symmetrization for fractional elliptic problems: a direct approach, Anomalous self-similar solutions of exponential type for the subcritical fast diffusion equation with weighted reaction, Exact solutions of a nonlinear diffusion equation on polynomial invariant subspace of maximal dimension, Unnamed Item, Extinction and non-extinction of solutions to a fast diffusion \(p\)-Laplace equation with logarithmic non-linearity, The well-posedness problem of an anisotropic porous medium equation with a convection term, Critical mass capacity for two-dimensional Keller–Segel model with nonlocal reaction terms, Unnamed Item, Bubbling and extinction for some fast diffusion equations in bounded domains, Finite difference schemes for the parabolic \(p\)-Laplace equation, On solutions of the fifth-order dispersive equations with porous medium type non-linearity, Multiple solutions for a class of anisotropic \(\vec{p}\)-Laplacian problems, Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities, Expansion of positivity for doubly nonlinear parabolic equations and its application, Asymptotic behaviour of blow-up solutions of the fast diffusion equation, Fractional Burgers equation with singular initial condition, Existence and stability of traveling waves for doubly degenerate diffusion equations, Crystalline surface diffusion flow for graph-like curves, Anisotropic fast diffusion equations, Elliptic gradient estimates for a nonlinear equation with Dirichlet boundary condition, Functional inequalities and applications to doubly nonlinear diffusion equations, Noncoercive diffusion equations with Radon measures as initial data, On the speed of decay of solutions to some partial differential equations, Homogenization of nonlinear nonlocal diffusion equation with periodic and stationary structure, Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation. I. Stratified groups, Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations, The Cauchy-Dirichlet problem for singular nonlocal diffusions on bounded domains, Cauchy-Dirichlet problems for the porous medium equation, Parabolic methods for ultraspherical interpolation inequalities, Doubly nonlinear parabolic equations with Robin boundary conditions, One-Dimensional Short-Range Nearest-Neighbor Interaction and Its Nonlinear Diffusion Limit, Rates of convergence to non-degenerate asymptotic profiles for fast diffusion via energy methods, Continuity up to the boundary for obstacle problems to porous medium type equations, Approaching critical decay in a strongly degenerate parabolic equation, Minimal \(L^p\)-solutions to singular sublinear elliptic problems, Asymptotic Behavior of Solutions Toward the Viscous Shock Waves to the Cauchy Problem for the Scalar Conservation Law with Nonlinear Flux and Viscosity, Topology optimization method with nonlinear diffusion, The Geometry of Diffusing and Self-Attracting Particles in a One-Dimensional Fair-Competition Regime, The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion, Existence of weak solutions for porous medium equation with a divergence type of drift term, Space-time homogenization for nonlinear diffusion, Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators, Ultra-contractivity for Keller-Segel model with diffusion exponent \(m>1-2/d\), Unnamed Item, Quantitative local and global a priori estimates for fractional nonlinear diffusion equations, Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type, Singular limits and properties of solutions of some degenerate elliptic and parabolic equations, Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type, Multi-valued, singular stochastic evolution inclusions, Classical solutions for a logarithmic fractional diffusion equation, The Gradient Discretization Method for Slow and Fast Diffusion Porous Media Equations, Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives, Superdiffusion in spin chains, Error Estimates for the Gradient Discretisation Method on Degenerate Parabolic Equations of Porous Medium Type, Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption, Radial equivalence for the two basic nonlinear degenerate diffusion equations, Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations, Capillary transport in paper porous materials at low saturation levels: normal, fast or superfast?, Radial equivalence and study of self-similarity for two very fast diffusion equations, Higher integrability for doubly nonlinear parabolic systems, Higher integrability for doubly nonlinear parabolic systems, Mathematical Analysis of a PDE-ODE Coupled Model of Mitochondrial Swelling with Degenerate Calcium Ion Diffusion, Uniqueness and time oscillating behaviour of finite points blow-up solutions of the fast diffusion equation, Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains, Book Review: Degenerate diffusions, Similarity solution to fractional nonlinear space-time diffusion-wave equation, Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications, Interplay of nonlinear diffusion, initial tails and Allee effect on the speed of invasions, Gradient estimates and entropy monotonicity formula for doubly nonlinear diffusion equations on Riemannian manifolds, Nonlinear parabolic equations with Robin boundary conditions and Hardy-Leray type inequalities, Optimal boundary regularity for fast diffusion equations in bounded domains, Smoothing effects for the filtration equation with different powers, The Fisher-KPP problem with doubly nonlinear ``fast diffusion, Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application, Asymptotic behaviour of solutions of the fast diffusion equation near its extinction time, Equilibria of homogeneous functionals in the fair-competition regime, Hamilton's gradient estimate for fast diffusion equations under geometric flow, Sobolev-type inequalities on Cartan-Hadamard manifolds and applications to some nonlinear diffusion equations, Cauchy problem and initial traces for fast diffusion equation with space-dependent source, Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations, Gradient inequality and convergence to steady-states of the normalized Ricci flow on surfaces, The Cauchy problem for the fast \(p\)-Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour, Singular extinction profiles of solutions to some fast diffusion equations, Marcinkiewicz regularity for singular parabolic \(p\)-Laplace type equations with measure data, Oscillatory decay in a degenerate parabolic equation, Regularizing properties of the twisted Kähler-Ricci flow, Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below, Existence and uniqueness of the solution for stochastic super-fast diffusion equations with multiplicative noise, Remark on the Cauchy problem for the evolution \(p\)-Laplacian equation, Reaction-diffusion systems with supercritical nonlinearities revisited, Decay properties of solutions toward a multiwave pattern to the Cauchy problem for the scalar conservation law with degenerate flux and viscosity, The Fisher-KPP problem with doubly nonlinear diffusion, Global asymptotics toward the rarefaction waves for solutions to the Cauchy problem of the scalar conservation law with nonlinear viscosity, Interior estimates for generalized Forchheimer flows of slightly compressible fluids, Proper spaces for the asymptotic convergence of solutions of porous medium equation, Travelling wave behaviour arising in nonlinear diffusion problems posed in tubular domains, Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms, On the sharp stability of critical points of the Sobolev inequality, Aronson-Bénilan estimates for the fast diffusion equation under the Ricci flow, On a partial boundary value condition of a porous medium equation with exponent variable, On solutions of a parabolic equation with nonstandard growth condition, Super fast vanishing solutions of the fast diffusion equation, Radial equivalence of nonhomogeneous nonlinear diffusion equations, Spatially monotone homoclinic orbits in nonlinear parabolic equations of super-fast diffusion type, Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics, The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour, Hipster random walks, Global structure of solutions toward the rarefaction waves for the Cauchy problem of the scalar conservation law with nonlinear viscosity, The fractional porous medium equation on the hyperbolic space, Long-time asymptotics for the porous medium equation: the spectrum of the linearized operator, Special asymptotics for a critical fast diffusion equation, Higher integrability for the singular porous medium system, Analytic approaches of the anomalous diffusion: a review, Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas, Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured Euclidean space, Anisotropic \(p\)-Laplacian evolution of fast diffusion type, Growing solutions of the fractional \(p\)-Laplacian equation in the fast diffusion range, Regularity estimates for the \(p\)-Sobolev flow, Diffusion processes on an interval under linear moment conditions, Extinction profile of the logarithmic diffusion equation, Boundary layer behavior of the non-Newtonian filtration equation with a small physical parameter, Existence and stability of the doubly nonlinear anisotropic parabolic equation, Sobolev and Hardy-Littlewood-Sobolev inequalities, Nonlinear flows and rigidity results on compact manifolds, Global estimates for generalized Forchheimer flows of slightly compressible fluids, Quasilinear parabolic and elliptic equations with singular potentials, The nonlocal porous medium equation: Barenblatt profiles and other weak solutions, The method of differential contractions, Properties of generalized Forchheimer flows in porous media, Global existence and blow-up of solutions for a non-Newton polytropic filtration system with special volumetric moisture content, Finite time extinction for stochastic sign fast diffusion and self-organized criticality, Asymptotic large time behavior of singular solutions of the fast diffusion equation, Existence of weak solutions of doubly nonlinear parabolic equations, Decay rate and radial symmetry of the exponential elliptic equation, Some recent advances in nonlinear diffusion on negatively-curved Riemannian manifolds: from barriers to smoothing effects, Rate of convergence to Barenblatt profiles for the fast diffusion equation, Pointwise estimates via parabolic potentials for a class of doubly nonlinear parabolic equations with measure data, Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions, Elliptic gradient estimates for the doubly nonlinear diffusion equation, The concavity of \(p\)-Rényi entropy power for doubly nonlinear diffusion equations and \(L^p\)-Gagliardo-Nirenberg-Sobolev inequalities, Smoothing effects and infinite time blowup for reaction-diffusion equations: an approach via Sobolev and Poincaré inequalities, Existence and large time behaviour of finite points blow-up solutions of the fast diffusion equation, \(q\)-moment estimates for the singular \(p\)-Laplace equation and applications, The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case, A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion, Doubly degenerate parabolic equation with time-dependent gradient source and initial data measures, Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case, Decay estimates for solutions of porous medium equations with advection, Modeling non-Darcian flow and solute transport in porous media with the Caputo-Fabrizio derivative, Regularity and time behavior of the solutions to weak monotone parabolic equations, Infinite-time concentration in aggregation-diffusion equations with a given potential, Improved regularity for the porous medium equation along zero level sets, Gradient estimates for nonlinear reaction-diffusion equations on Riemannian manifolds, The concavity of Rényi entropy power for the parabolic \(p\)-Laplace equations and applications, Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal degenerate parabolic equation arising in game theory, On the Hölder regularity for obstacle problems to porous medium type equations, Infinite-time incompleteness of noncompact Yamabe flow, Self-improving property of the fast diffusion equation, The self-improving property of higher integrability in the obstacle problem for the porous medium equation, Solving a nonlinear variation of the heat equation: self-similar solutions of the second kind and other results, Asymptotic behavior and regularity properties of strongly nonlinear parabolic equations, A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation, Reverse Hardy-Littlewood-Sobolev inequalities, A multi-dimension blow-up problem to a porous medium diffusion equation with special medium void, Uniqueness of instantaneously complete Ricci flows, Existence and supercontractive estimates for parabolic-elliptic systems, 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 the second-order regularity of solutions to the parabolic \(p\)-Laplace equation, Relation between solutions and initial values for double-nonlinear diffusion equation, Gradient estimates for singular parabolic \(p\)-Laplace type equations with measure data, Large time behavior for the fast diffusion equation with critical absorption, Type I ancient compact solutions of the Yamabe flow, Very slow stabilization for a nonlinear Fokker-Planck equation, Asymptotic analysis of a doubly nonlinear diffusion equation, Option pricing with linear market impact and nonlinear Black-Scholes equations, Stability/nonstability properties of renormalized/entropy solutions for degenerate parabolic equations with \(L^1\)/measure data, The boundary value condition of an evolutionary \(p(x)\)-Laplacian equation, Decay estimates for nonlocal problems via energy methods, A new contraction family for porous medium and fast diffusion equations, Periodic solutions to fast diffusion equations with nonlipschitz convective terms, Extinction for a singular diffusion equation with strong gradient absorption revisited, Solutions with moving singularities for equations of porous medium type, Sharp boundedness and continuity results for the singular porous medium equation, Anomalous large-time behaviour of the \(p\)-Laplacian flow in an exterior domain in low dimension, Rate of convergence to separable solutions of the fast diffusion equation, Classification of certain qualitative properties of solutions for the quasilinear parabolic equations, Global positivity estimates and Harnack inequalities for the fast diffusion equation, Fujita phenomenon in inhomogeneous fast diffusion system, Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces, Regularity of solutions of the fractional porous medium flow, Mathematical treatment of the discharge of a laminar hot gas in a stagnant colder atmosphere, Some properties of generalized Fisher information in the context of nonextensive thermostatistics, Hardy-Poincaré inequalities and applications to nonlinear diffusions, Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent \(m > 0\), Large time behavior for a quasilinear diffusion equation with critical gradient absorption, The classification of locally conformally flat Yamabe solitons, Decay properties of solutions to the Cauchy problem for the scalar conservation law with nonlinearly degenerate viscosity, A fractional porous medium equation, A kinetic model for the formation of swarms with nonlinear interactions, Radon measure-valued solutions of nonlinear strongly degenerate parabolic equations, Positivity, decay, and extinction for a singular diffusion equation with gradient absorption, Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds., Nonlinear diffusion of dislocation density and self-similar solutions, Extinction, decay and blow-up for Keller-Segel systems of fast diffusion type, Convergence of invariant measures for singular stochastic diffusion equations, Asymptotic time behaviour for non-autonomous degenerate parabolic problems with forcing term, Gradient estimates for porous medium and fast diffusion equations by martingale method, Laplacian cut-offs, porous and fast diffusion on manifolds and other applications, Flatness implies smoothness for solutions of the porous medium equation, Complicated asymptotic behavior of solutions for porous medium equation in unbounded space, Pointwise gradient estimates, The fast diffusion equation with measure data, Convergence of the Dirichlet solutions of the very fast diffusion equation, A class of nonlinear degenerate elliptic equations related to the Gauss measure, Gradient estimates for \(u_t = \Delta F(u)\) on manifolds and some Liouville-type theorems, Quantitative a priori estimates for fast diffusion equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuity, Nonlinear measure data problems, Gradient estimates for doubly nonlinear diffusion equations, Cauchy problem for doubly nonlinear parabolic equations with initial data measures, Highly time-oscillating solutions for very fast diffusion equations, Time periodic solutions of the diffusive Nicholson blowflies equation with delay, A local discontinuous Galerkin method for a doubly nonlinear diffusion equation arising in shallow water modeling, The Penrose-Fife phase-field model, Behaviour near extinction for the fast diffusion equation on bounded domains, Cauchy problem for doubly degenerate parabolic equation with gradient source, A new approach to decay estimates - application to a nonlinear and degenerate parabolic PDE, Classical and quantum mechanical models of many-particle systems. Abstracts from the workshop held December 3--9, 2017, Finite time extinction of solutions to fast diffusion equations driven by linear multiplicative noise, Optimal estimates for fractional fast diffusion equations, Fundamental solution and long time behavior of the porous medium equation in hyperbolic space, Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour, Time regularity and long-time behavior of parabolic \(p\)-Laplace equations on infinite graphs, On uniform and decay estimates for unbounded solutions of partial differential equations, One-dimensional super-fast diffusion: persistence versus extinction revisited -- extinction at spatial infinity, Moser-Nash kernel estimates for degenerate parabolic equations, Symmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities, Quantitative asymptotic estimates for evolution problems, Yamabe flow: steady solitons and type II singularities, Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D, Global behaviour of solutions of the fast diffusion equation, Stochastic porous media equations in \(\mathbb R^d\), Hamilton's gradient estimates of porous medium and fast diffusion equations, Approximate analytical solutions of the nonlinear reaction-diffusion-convection problems, Barenblatt profiles for a nonlocal porous medium equation, Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems, Large time behaviour of solutions to a class of non-autonomous, degenerate parabolic equations, On the equivalence between \(p\)-Poincaré inequalities and \(L^r\)-\(L^q\) regularization and decay estimates of certain nonlinear evolutions, Extinction and decay estimates of solutions for a class of doubly degenerate equations, Local smoothing effects, positivity, and Harnack inequalities for the fast \(p\)-Laplacian equation, Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold, Asymptotic decay and non-rupture of viscous sheets, Pattern formation in a flux limited reaction-diffusion equation of porous media type, Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds, Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian, Backward estimates for nonnegative solutions to a class of singular parabolic equations, Hamilton's gradient estimates for fast diffusion equations under the Ricci flow, Measure-valued solutions and the phenomenon of blow-down in logarithmic diffusion, Stability on time-dependent domains, Asymptotic analysis of the \(p\)-Laplacian flow in an exterior domain, Measure-valued solutions of nonlinear parabolic equations with logarithmic diffusion, Asymptotics of the fast diffusion equation via entropy estimates, Total variation flow and sign fast diffusion in one dimension, Singular limit and exact decay rate of a nonlinear elliptic equation, On the stochastic \(p\)-Laplace equation, Ricci flow on surfaces of revolution: an extrinsic view, Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations, Existence of Neumann and singular solutions of the fast diffusion equation, From the highly compressible Navier-Stokes equations to the porous medium equation -- rate of convergence, The boundary degeneracy of a singular diffusion equation, Positivity of self-similar solutions of doubly nonlinear reaction-diffusion equations