Some recent advances in nonlinear diffusion on negatively-curved Riemannian manifolds: from barriers to smoothing effects

DOI10.1007/s40574-020-00238-5zbMath1462.35181OpenAlexW3036185162WikidataQ115372770 ScholiaQ115372770MaRDI QIDQ2024157

Matteo Muratori

Publication date: 3 May 2021

Published in: Bollettino dell'Unione Matematica Italiana (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11311/1142855

zbMATH Keywords

Cartan-Hadamard manifoldsequations of porous-medium

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) Quasilinear parabolic equations (35K59) PDEs on manifolds (35R01)

Related Items (1)

Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds

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
• Fundamental solution and long time behavior of the porous medium equation in hyperbolic space
• Smoothing effects for the porous medium equation on Cartan-Hadamard manifolds
• Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures
• Long time behavior for the inhomogeneous PME in a medium with slowly decaying density
• Sublinear elliptic equations in \(\mathbb{R}{}^ n\)
• The porous medium equation on Riemannian manifolds with negative curvature: the superquadratic case
• The porous medium equation with large initial data on negatively curved Riemannian manifolds
• The Dirichlet problem for the porous medium equation in bounded domains. Asymptotic behavior
• Sharp short and long time \(L^{\infty }\) bounds for solutions to porous media equations with homogeneous Neumann boundary conditions
• Asymptotic behavior of the solutions of the inhomogeneous porous medium equation with critical vanishing density
• The porous medium equation with measure data on negatively curved Riemannian manifolds
• Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density
• Fast diffusion flow on manifolds of nonpositive curvature
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• Asymptotics of the porous media equation via Sobolev inequalities
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

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