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Stability of the separable solution for fast diffusion
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Outgoing claims: the papers this work cites, builds on, or argues with.
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Remarks on some quasilinear elliptic equations
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Theory and numerical simulation on plasma diffusion across a magnetic field
inferredcites →https://doi.org/10.1063/1.523190openalex-snapshot
Evolution of a stable profile for a class of nonlinear diffusion equations with fixed boundaries
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Evolution of a stable profile for a class of nonlinear diffusion equations. II
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Diffusion coefficient scaling in the Wisconsin levitated octupole
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Theory of nonlinear diffusion of plasma across the magnetic field of a toroidal multipole
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Applications of functional analysis in mathematical physics
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains
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Uniqueness and nonuniqueness for positive radial solutions of Δu + f(u, r) = 0
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Extinction of solutions to a class of fast diffusion systems with nonlinear sources
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Asymptotics Near Extinction for Nonlinear Fast Diffusion on a Bounded Domain
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Extinction Profiles for the Sobolev Critical Fast Diffusion Equation in Bounded Domains. I. One Bubble Dynamics
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Stability of Non-Isolated Asymptotic Profiles for Fast Diffusion
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Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations
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The fractional p-Laplacian evolution equation in $${\mathbb {R}}^N$$ in the sublinear case
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Asymptotic analysis of extinction behaviour in fast nonlinear diffusion
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Energy Solutions of the Cauchy–Dirichlet Problem for Fractional Nonlinear Diffusion Equations
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Rate of convergence to separable solutions of the fast diffusion equation
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Large time behaviour of solutions of the porous medium equation in bounded domains
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Lower bound estimates and separable solutions for homogeneous equations of evolution in Banach space
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Uniqueness of solutions of nonlinear Dirichlet problems
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Diffusivity versus absorption through the boundary
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The first boundary value problem for −u″ = λup
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On nonexistence of similarity solutions
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Semi-discretization in time of a fast diffusion equation
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A non-linear boundary value problem of ignition by radiation
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Stabilization of solutions of nonlinear and degenerate evolution equations
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On a nonlinear singular diffusion problem: convergence to a traveling wave
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The asymptotic profile of solutions of a class of doubly nonlinear equations
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Remarks on a singular diffusion equation
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Density-Dependent Interaction–Diffusion Systems
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Parabolic approach to nonlinear elliptic eigenvalue problems
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Long-time behavior for the porous medium equation with small initial energy
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Regularity of solutions to the Dirichlet problem for fast diffusion equations
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Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli
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Sobolev and Hardy–Littlewood–Sobolev inequalities
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Global positivity estimates and Harnack inequalities for the fast diffusion equation
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Hölder estimates for singular non-local parabolic equations
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Self-improving property of the fast diffusion equation
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Singular extinction profiles of solutions to some fast diffusion equations
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Optimal rate of convergence to nondegenerate asymptotic profiles for fast diffusion in domains
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Regularity in Sobolev spaces for the fast diffusion and the porous medium equation
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A nonlinear singular diffusion equation with source
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A variational approach to stochastic nonlinear parabolic problems
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Existence and uniqueness of the solution for stochastic super-fast diffusion equations with multiplicative noise
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Behaviour near extinction for the Fast Diffusion Equation on bounded domains
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Stability of the separable solutions for a nonlinear boundary diffusion problem
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Asymptotic time behaviour for non-autonomous degenerate parabolic problems with forcing term
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Existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains
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The Cauchy–Dirichlet problem for the fast diffusion equation on bounded domains
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Extremals for Poincaré-Sobolev sharp constants in Steiner symmetric sets
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A doubly nonlinear parabolic equation with nonlinear perturbation under relaxed growth and exponent conditions
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Convergence of invariant measures for singular stochastic diffusion equations
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Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents
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The First Boundary Value Problem for Nonlinear Diffusion
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On the asymptotic behavior of solutions to a class of degenerate parabolic problems of Neumann type
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Numerical solution of fast diffusion or slow diffusion equations
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Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights
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Gradient estimates for degenerate diffusion equations II
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Asymptotic results for nonlinear outdiffusion
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Nonlinear thermal evolution in an inhomogeneous medium
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Exponential convergence for nonlinear diffusion problems with positive lateral boundary conditions
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Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
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Extinction and non-extinction for a polytropic filtration equation with a nonlocal source
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Extinction and non-extinction for a polytropic filtration system with non-linear sources
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Asymptotic behavior of the plasma equation with homogeneous dirichlet boundary condition and non-negative initial data
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On a nonlinear singular diffusion problem:existence and uniqueness
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The diffusive limit of two velocity models: The porous medium equation
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LPBounds of solutions of reaction-diffusion equations
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Finite extinction time for a class of non-linear parabolic equations
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A Nonlinear heat equation with singular diffusivity
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On the cauchy problem for a very fast diffusion equation
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Exact results for the nonlinear diffusion equations delta u/ delta t= delta / delta x(u -4/3 delta u/ delta x) and delta u/ delta t- delta / delta x(u -2/3 delta u/ delta x)
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Fast diffusion equation with critical Sobolev exponent in a ball
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Bubbling and extinction for some fast diffusion equations in bounded domains
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Interior and Boundary Regularity of Solutions to a Plasma Type Equation
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Behaviour of the velocity of one-dimensional flows in porous media
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Singular Behavior in Nonlinear Parabolic Equations
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Boundary Behavior of the Fast Diffusion Equation
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Harnack Estimates and Extinction Profile for Weak Solutions of Certain Singular Parabolic Equations
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Existence and nonexistence of global positive solutions to nonlinear diffusion problems with nonlinear absorption through the boundary
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Error Estimates for a Nonlinear Degenerate Parabolic Problem
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Numerical solution of a fast diffusion equation
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Smoothing and Decay Estimates for Nonlinear Diffusion Equations
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Copyright Page
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Introduction
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780199202973.003.0002openalex-snapshot
Preliminaries
inferred← citeshttps://doi.org/10.1093/acprof:oso/9780199202973.003.0003openalex-snapshot
Smoothing effect and time decay. Data inL1 (Rn) orM(Rn)
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Smoothing effect and time decay fromLporMp
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Lower bounds, contractivity, error estimates, and continuity
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Subcritical range of the FDE. Critical line. Extinction. Backward effect
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Improved analysis of the critical line. Delayed regularity
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Extinction rates and asymptotics for 0 <m
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Logarithmic diffusion in 2D and intermediate 1D range
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Superfast FDE
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Summary of main results for the PME/FDE
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Evolution equations of thep-Laplacian type
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Some analysis topics
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Particles and speeds
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Some Riemannian geometry
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Some extensions and parallel topics
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Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type
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On homogeneous evolution equation in a Banach space
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On Homogeneous Distributed Parameter Systems
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Extinction behavior for the fast diffusion equations with critical exponent and Dirichlet boundary conditions
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Radial fast diffusion on the hyperbolic space
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New Exact Solutions of the Diffusion Equation with Power Nonlinearity
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Asymptotic Behavior of Solutions of a Nonlinear Diffusion Equation
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Finite Element Approximation of the Fast Diffusion and the Porous Medium Equations
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The Evolution of Singularities in Fast Diffusion Equations: Infinite-Time Blow-Down
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Optimal Decay Estimates for Time-Fractional and Other NonLocal Subdiffusion Equations via Energy Methods
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The Gradient Discretization Method for Slow and Fast Diffusion Porous Media Equations
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Darcy's Law and the Theory of Shrinking Solutions of Fast Diffusion Equations
inferred← citeshttps://doi.org/10.1137/s0036141091217731openalex-snapshot
On a Nonlinear Parabolic Problem Arising in Some Models Related to Turbulent Flows
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The Degeneracy of a Fast-Diffusion Equation and Stability
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POROUS MEDIUM FLOW IN A TUBE: TRAVELING WAVES AND KPP BEHAVIOR
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Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations
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Critical extinction exponents for a fast diffusion equation with nonlocal source and absorption
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Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
inferred← citeshttps://doi.org/10.1214/ecp.v16-1643openalex-snapshot
Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts
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Optimal boundary regularity for fast diffusion equations in bounded domains
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On a class of fully nonlinear parabolic equations
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Optimal regularity and fine asymptotics for the porous medium equation in bounded domains
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On solutions of a perturbed fast diffusion equation
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Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion
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Stability analysis of asymptotic profiles for fast diffusion equations
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Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the $p$-Laplacian
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The asymptotic behavior of solutions of some nonlinear initial-boundary value problems of parabolic type
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Numerical interfaces in nonlinear diffusion equations with finite extinction phenomena
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An Ill-Posed Estimate of Positive Solutions of a Degenerate Nonlinear Parabolic Equation
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A continuum of extinction rates for the fast diffusion equation
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The Cauchy-Dirichlet problem for singular nonlocal diffusions on bounded domains
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Finite-dimensional leading order dynamics for the fast diffusion equation near extinction
inferred← citeshttps://doi.org/10.3934/dcdss.2014.7.725openalex-snapshot
Special asymptotics for a critical fast diffusion equation
inferred← citeshttps://doi.org/10.4134/bkms.2014.51.1.055openalex-snapshot
EXTINCTION AND NON-EXTINCTION OF SOLUTIONS TO A FAST DIFFUSIVE p-LAPLACE EQUATION WITH A NONLOCAL SOURCE
inferred← citeshttps://doi.org/10.4171/ifb/90openalex-snapshot
Nonlinear diffusion and image contour enhancement
inferred← citeshttps://doi.org/10.4171/zaa/958openalex-snapshot
On some Improperly Posed Problem for a Degenerate Nonlinear Parabolic Equation
inferred← citeshttps://doi.org/10.4310/mrl.2011.v18.n6.a1openalex-snapshot
Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion
inferred← citeshttps://doi.org/10.48550/arxiv.1905.01785openalex-snapshot
The gradient discretisation method for slow and fast diffusion porous media equations
inferred← citeshttps://doi.org/10.48550/arxiv.2006.01308openalex-snapshot
Extinction behaviour for the fast diffusion equations with critical exponent and Dirichlet boundary conditions
inferred← citeshttps://doi.org/10.5565/publmat_19180_08openalex-snapshot
Resultados y métodos sobre la propiedad de extinción en tiempo finito para ecuaciones de evolución
inferred← citeshttps://doi.org/10.57262/ade/1355867324openalex-snapshot
Localized large reaction for a non-linear reaction-diffusion system
inferred← citeshttps://doi.org/10.57262/die/1370378432openalex-snapshot
Large time behavior of the maximal solution of equation $u_t=(u^{m-1}u_x)_x$ with $-1
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