Fine properties of solutions to the Cauchy problem for a fast diffusion equation with Caffarelli-Kohn-Nirenberg weights

DOI10.4171/AIHPC/42MaRDI QIDQ2693543

Nikita Simonov, Matteo Bonforte

Publication date: 21 March 2023

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.09967

zbMATH Keywords

fast diffusion equationasymptotic behaviourtail behaviourglobal Harnack inequalitiesBarenblatt fundamental solutionCaffarelli-Kohn-Nirenberg weights

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45) Singular parabolic equations (35K67) Quasilinear parabolic equations (35K59)

Related Items

Anisotropic fast diffusion equations, Stability of the separable solutions for a nonlinear boundary diffusion problem

Cites Work

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• On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density
• Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincaré inequalities
• Pointwise estimates for the fundamental solutions of a class of singular parabolic problems
• Fundamental solution and long time behavior of the porous medium equation in hyperbolic space
• Symmetry for extremal functions in subcritical Caffarelli-Kohn-Nirenberg inequalities
• Optimal existence and uniqueness theory for the fractional heat equation
• Radial symmetry and symmetry breaking for some interpolation inequalities
• Weighted fast diffusion equations I: sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities
• Weighted fast diffusion equations II: sharp asymptotic rates of convergence in relative error by entropy methods
• Backward estimates for nonnegative solutions to a class of singular parabolic equations
• Proprietà di alcune classi di funzioni in più variabili
• Global positivity estimates and Harnack inequalities for the fast diffusion equation
• Potential theory and optimal convergence rates in fast nonlinear diffusion
• A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media
• The Cauchy problem for the inhomogeneous porous medium equation
• Hardy-Poincaré inequalities and applications to nonlinear diffusions
• Rigidity results with applications to best constants and symmetry of Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities
• Nonexistence of solutions for nonlinear heat equations of fast-diffusion type
• A well posed problem in singular Fickian diffusion
• The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium
• Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold
• Long time behavior for the inhomogeneous PME in a medium with slowly decaying density
• Asymptotics of the fast diffusion equation via entropy estimates
• Asymptotic behaviour of solutions of some semilinear parabolic problems
• On the Cauchy problem for a class of parabolic equations with variable density
• On nonlinear parabolic equations of very fast diffusion
• A convexity principle for interacting gases
• Asymptotic behaviour near finite-time extinction for the fast diffusion equation
• An intrinsic metric approach to uniqueness of the positive Cauchy problem for parabolic equations
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• The maximal solution of the logarithmic fast diffusion equation in two space dimensions
• Asymptotic behaviour for the porous medium equation posed in the whole space.
• Weighted interpolation inequalities: a perturbation approach
• Flatness implies smoothness for solutions of the porous medium equation
• Quantitative a priori estimates for fast diffusion equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuity
• Type II ancient compact solutions to the Yamabe flow
• Fast diffusion to self-similarity: Complete spectrum, long-time asymptotics, and numerology
• Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type.
• Hölder regularity and Harnack inequality for degenerate parabolic equations related to Caffarelli-Kohn-Nirenberg inequalities
• On a singular diffusion equation
• Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model
• Asymptotic behavior of the solutions of the inhomogeneous porous medium equation with critical vanishing density
• The fractional \(p\)-Laplacian evolution equation in \(\mathbb{R}^N\) in the sublinear case
• The Cauchy problem for the fast \(p\)-Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour
• The evolution fractional p-Laplacian equation in \(\mathbb{R}^N\). Fundamental solution and asymptotic behaviour
• Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density
• Extinction profile of complete non-compact solutions to the Yamabe flow
• Fast diffusion flow on manifolds of nonpositive curvature
• Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density
• Improved interpolation inequalities, relative entropy and fast diffusion equations
• Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for \(u_t = \Delta\varphi(u)\)
• The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions
• Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
• A fast regularisation of a Newtonian vortex equation
• 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)}
• On a singular heat equation with dynamic boundary conditions
• Radial fast diffusion on the hyperbolic space
• Poincaré inequalities for linearizations of very fast diffusion equations
• A Harnack inequality for degenerate parabolic equations
• On the extinction profile of solutions to fast diffusion
• 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
• Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
• The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium
• Propagation of thermal waves in an inhomogeneous medium
• Non-linear diffusion in a finite mass medium
• Nonlinear thermal evolution in an inhomogeneous medium
• Harnack's Inequality for Degenerate Parabolic Equations
• On the behavior of the solutions of degenerate parabolic equations
• The Filtration Equation in a Class of Functions Decreasing at Infinity
• Asymptotics of the Fast-Diffusion Equation with Critical Exponent
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• Results on Parabolic Equations Related to Some Caffarelli--Kohn--Nirenberg Inequalities
• Fine Asymptotics for Fast Diffusion Equations
• On Fast-Diffusion Equations with Infinite Equilibrium Entropy and Finite Equilibrium Mass
• Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
• On Hölder continuity of solutions of doubly nonlinear parabolic equations with weight
• Higher-order time asymptotics of fast diffusion in Euclidean space: A dynamical systems approach
• Second-order asymptotics for the fast-diffusion equation
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities