scholarly journals Existence and maximalLp-regularity of solutions for the porous medium equation on manifolds with conical singularities

2016 ◽  
Vol 41 (9) ◽  
pp. 1441-1471 ◽  
Author(s):  
Nikolaos Roidos ◽  
Elmar Schrohe
Keyword(s):  
Porous Medium ◽  
Porous Medium Equation ◽  
Regularity Of Solutions ◽  
Conical Singularities ◽  
Medium Equation ◽  
Manifolds With Conical Singularities

scholarly journals Regularity of solutions of a fractional porous medium equation

2020 ◽  
Vol 22 (4) ◽  
pp. 401-442
Author(s):  
Cyril Imbert ◽  
Rana Tarhini ◽  
François Vigneron
Keyword(s):  
Porous Medium ◽  
Porous Medium Equation ◽  
Regularity Of Solutions ◽  
Medium Equation

Regularity of solutions and interfaces of the porous medium equation via local estimates

1989 ◽  
Vol 112 (1-2) ◽  
pp. 1-13 ◽  
Author(s):  
Juan Luis Vazquez
Keyword(s):  
Porous Medium ◽  
Porous Medium Equation ◽  
Regularity Of Solutions ◽  
Pressure Function ◽  
Medium Equation ◽  
Moving Interfaces ◽  
Local Solutions

SynopsisWe prove C∞ regularity for moving interfaces of local solutions of the porous medium equation as well as C∞ lateral regularity for the pressure function near such an interface.

Harnack estimates for a kind of porous medium equation

2021 ◽  
Vol 115 ◽  
pp. 106978
Author(s):  
Feida Jiang ◽  
Xinyi Shen ◽  
Hui Wu
Keyword(s):  
Porous Medium ◽  
Porous Medium Equation ◽  
Medium Equation ◽  
Harnack Estimates

scholarly journals Global existence of solutions and smoothing effects for classes of reaction–diffusion equations on manifolds

2021 ◽  
Author(s):  
Gabriele Grillo ◽  
Giulia Meglioli ◽  
Fabio Punzo
Keyword(s):  
Porous Medium ◽  
Global Existence ◽  
Source Term ◽  
Reaction Diffusion ◽  
Porous Medium Equation ◽  
Variable Density ◽  
Reaction Diffusion Equations ◽  
Medium Equation ◽  
Global Existence Of Solutions ◽  
Smoothing Effects

AbstractWe consider the porous medium equation with a power-like reaction term, posed on Riemannian manifolds. Under certain assumptions on p and m in (1.1), and for small enough nonnegative initial data, we prove existence of global in time solutions, provided that the Sobolev inequality holds on the manifold. Furthermore, when both the Sobolev and the Poincaré inequalities hold, similar results hold under weaker assumptions on the forcing term. By the same functional analytic methods, we investigate global existence for solutions to the porous medium equation with source term and variable density in $${{\mathbb {R}}}^n$$ R n .

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