Potential theory and optimal convergence rates in fast nonlinear diffusion
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Publication:864177
DOI10.1016/j.matpur.2006.01.002zbMath1112.35025OpenAlexW2118779383MaRDI QIDQ864177
Robert J. McCann, Yong-Jung Kim
Publication date: 13 February 2007
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matpur.2006.01.002
Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)
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Cites Work
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- Complexity of large time behaviour of evolution equations with bounded data
- Contractions in the 2-Wasserstein length space and thermalization of granular media
- Fundamental solutions and asymptotic behaviour for the p-Laplacian equations
- Non-negative solutions to fast diffusions
- Eventual \(C^{\infty}\)-regularity and concavity for flows in one- dimensional porous media
- Non-negative solutions of generalized porous medium equations
- On the Cauchy problem for \(u_t= \Delta\log u\) in higher dimensions
- The Cauchy problem for variable coefficient porous medium equations
- Asymptotic behaviour near finite-time extinction for the fast diffusion equation
- Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to \(N\)-waves
- Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
- Asymptotic behaviour for the porous medium equation posed in the whole space.
- Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
- Fast diffusion to self-similarity: Complete spectrum, long-time asymptotics, and numerology
- All time \(C^\infty\)-regularity of the interface in degenerate diffusion: A geometric approach
- Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities
- The asymptotic behaviour of the solution of the filtration equation
- Sharp decay rates for the fastest conservative diffusions
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- On the extinction profile for solutions of $u_t=\Delta u^{(N-2)/(N+2)}
- Nonradial solvability structure of super-diffusive nonlinear parabolic equations
- Poincaré inequalities for linearizations of very fast diffusion equations
- Asymptotic Behaviour and Propagation Properties of the One-Dimensional Flow of Gas in a Porous Medium
- Non-negative solutions of theo porous medium eqation
- Geometrical properties of solutions of the Porous Medium Equation for large times
- Strict contractivity of the 2-Wasserstein distance for the porous medium equation by mass-centering
- Nonnegative Solutions of the Initial-Dirichlet Problem for Generalized Porous Medium Equations in Cylinders
- A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. I
- A Lyapunov functional for the evolution of solutions to the porous medium equation to self-similarity. II
- The Cauchy Problem for u t = Δu m When 0 < m < 1
- The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium
- Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
- Asymptotic Behaviour of Solutions of the Porous Medium Equation with Changing Sign
- Weak Solutions of the Porous Medium Equation in a Cylinder
- Weak Solutions of the Porous Medium Equation
- A Nonlinear heat equation with singular diffusivity
- On singular diffusion equations with applications to self‐organized criticality
- On the rate of convergence and asymptotic profile of solutions to the viscous burgers equations
- Asymptotics of the Fast-Diffusion Equation with Critical Exponent
- Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
- Self-similar behaviour for the equation of fast nonlinear diffusion
- Fine Asymptotics for Fast Diffusion Equations
- Self‐similar Asymptotics for Linear and Nonlinear Diffusion Equations
- On Fast-Diffusion Equations with Infinite Equilibrium Entropy and Finite Equilibrium Mass
- Phase transitions and symmetry breaking in singular diffusion
- Second-order asymptotics for the fast-diffusion equation
- DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
- Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
