The porous medium equation with large data on Cartan-Hadamard manifolds under general curvature bounds

DOI10.3934/dcds.2022104zbMath1518.35453arXiv2202.08727OpenAlexW4289827005MaRDI QIDQ6102549

Gabriele Grillo, Matteo Muratori, Fabio Punzo

Publication date: 23 June 2023

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.08727

zbMATH Keywords

blow-upporous medium equationcurvature boundslarge datastochastic completenessCartan-Hadamard manifolds

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Elliptic equations on manifolds, general theory (58J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order parabolic equations (35K15) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs on manifolds (35R01)

Related Items (1)

Some functional properties on Cartan-Hadamard manifolds of very negative curvature

Cites Work

• Function theory on manifolds which possess a pole
• Yamabe-type equations on complete, noncompact manifolds
• Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds
• 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
• Gradient estimates and differential Harnack inequalities for a nonlinear parabolic equation on Riemannian manifolds
• Nonlinear characterizations of stochastic completeness
• Uniqueness of very weak solutions for a fractional filtration equation
• The Initial Trace of a Solution of the Porous Medium Equation
• Stabilization of solutions of a degenerate nonlinear diffusion problem
• Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Fast diffusion on noncompact manifolds: Well-posedness theory and connections with semilinear elliptic equations
• Porous medium equations on manifolds with critical negative curvature: unbounded initial data
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