The porous medium equation on Riemannian manifolds with negative curvature: the superquadratic case

DOI10.1007/s00208-018-1680-1zbMath1411.35261arXiv1710.06399OpenAlexW2799198379WikidataQ115388916 ScholiaQ115388916MaRDI QIDQ1741815

Gabriele Grillo, Matteo Muratori, Juan Luis Vazquez

Publication date: 7 May 2019

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.06399

zbMATH Keywords

Riemannian manifoldporous medium equationnegative curvatureheat flow

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) 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 (9)

Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation ⋮ Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below ⋮ The Liouville theorem of a torsion system and its application to symmetry group of a porous medium type equation on symmetric spaces ⋮ Nonlinear characterizations of stochastic completeness ⋮ The porous medium equation with large data on Cartan-Hadamard manifolds under general curvature bounds ⋮ The fractional porous medium equation on the hyperbolic space ⋮ Some recent advances in nonlinear diffusion on negatively-curved Riemannian manifolds: from barriers to smoothing effects ⋮ Long-time behavior for the porous medium equation with small initial energy ⋮ Fast diffusion on noncompact manifolds: Well-posedness theory and connections with semilinear elliptic equations

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