Asymptotics of the porous media equation via Sobolev inequalities

By Matteo Bonforte, G. Grillo. 2005

62 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a9046697b734afab9e8330d03d77cf688cca7a82

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Existence and maximal Lp-regularity of solutions for the porous medium equation on manifolds with conical singularities (2015, background): “While traditionally treated on domains inRn, the porous medium equation has also been considered on closed compact and noncompact manifolds; we refer for this to Bonforte andGrillo [3], Huang et al.”
Fast diffusion flow on manifolds of nonpositive curvature (2008, background): “Certain analogues of this kind of correspondence have been investigated in several nonlinear setting in the papers [10], [3], [4] [5].”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “• Work on the Porous Medium Equation on manifolds was done in the 2000s, like [43], [244]; fast diffusion was treated in [44]; general Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds were obtained in [187].”
Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincar\'e inequalities (2012, background): “The most important difference with respect to the present setting lies in the fact that in [9] the validity of the (classical) Sobolev inequality was assumed to hold in W 1,2(Ω; ν, μ), where dν = dμ both coincide with the Riemannian measure on the manifold considered.”
On decay estimates (2009, background): “Finally, we observe that in [5], [ 7 ]–[10] ultracontractive estimates to solutions of p-Laplacian, porous media and fast diffusion equations are studied on Riemannian manifolds proving that the Sobolev inequality is equivalent to the ultracontractive bounds for a large number of parameters p and m ”
The Porous Medium Equation: Mathematical Theory (2006, unknown): “The Porous Medium Equation posed on a Riemannian Manifold, [413, 121].”