Fast diffusion flow on manifolds of nonpositive curvature

By Matteo Bonforte, G. Grillo, Juan Luis V'azquez. 2008

69 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/325f4a000bbbb66707d192bb6fc3fdffc244824c

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Laplacian cut-offs, porous and fast diffusion on manifolds and other applications (2016, methodology): “2) which is called Porous Medium Equation (PME) when the exponent m > 1 and Fast Diffusion Equation (FDE) when 0 < m < 1, has been widely studied in the Euclidean setting (see [35] and [36] for detailed surveys), and, in recent years, several papers studied the properties of the solutions of those e”
Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincar\'e inequalities (2012, unknown): “[9, 10, 11, 46, 12] and references quoted therein).”
Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation (2009, unknown): “Following ideas from [9] and [10], we consider a function f ∈ W 1,p 0 (Ω), and we apply the Poincaré, Sobolev and Hölder inequalities as follows: ‖f‖q ≤ ‖f‖p‖f‖ p∗ ≤ P θ ΩS p ‖∇f‖p, (7.”
Classification of radial solutions to the Emden–Fowler equation on the hyperbolic space (2011, background): “1) might be relevant for the study of the fine asymptotics of the solutions to the corresponding evolutionary problem ut = um , with 1 > m = (1)p , as initiated in [6], in the spirit of the recent results given in [7].”
Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations (2008, background): “These results can be extended to different domains or manifolds in a straightforward way, the only important thing is to have global Sobolev and Poincaré inequalities, as already studied by the authors in [7], in the case of Riemannian manifolds with nonpositive curvature Using this bound, we can no”