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C ∞-Regularity for the Porous Medium Equation [PDF]

Mathematische Zeitschrift, 1986
On etablit un resultat de regularite optimale pour l'equation d'un milieu poreux u t -(u m ) xx =0, x∈R, t>0, u(., 0)=u 0 pour m>1 et la donnee initiale u 0 positive continue a support compact ...
Höllig, K., Kreiss, H.-O.
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A Porous Medium Equation with Variable Nonlinearity

2015
We devote this chapter to study the homogeneous Dirichlet problem for the semilinear parabolic equation which generalizes the Porous Medium Equation.
Stanislav Antontsev, Sergey Shmarev
openaire   +1 more source

Flux diffusion and the porous medium equation

Physica C: Superconductivity, 1997
Abstract Flux-flow problems in slabs and cylinders, and flux-creep problems in slabs, simplified, reduce to the porous medium equation with possible sign changes. The equation's known self-similar solutions apply exactly or asymptotically if the boundary conditions are right.
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An Inverse Problem for Porous Medium Equation

1996
An inverse problem for a nonlinear degenerate diffusion equation is considered. We look for unknown coefficient a(u) of the equation u t = (a(u(u x ) x with zero initial values and nonmonotone impulse-like Dirichlet boundary condition. Measurements in an interior point x 0 are taken as overposed data. An optimization approach is used.
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Extension of Ergun Equation for the Calculation of the Flow Resistance in Porous Media With Higher Porosity and Open-Celled Structure

Applied Thermal Engineering, 2020
Xiangyang Liu, Jimin Xu
exaly  

Asymptotic Behaviour for the Porous Medium Equation Posed in the Whole Space

Journal of Evolution Equations, 2003
Juan Luis Vázquez
exaly  

Blowup of Solutions to a Porous Medium Equation With Nonlocal Boundary Condition

Applied Mathematics and Computation, 2007
Zhaoyin Xiang, Chunlai Mu, Yulan Wang
exaly  

Existence and Maximal Lp-Regularity of Solutions for the Porous Medium Equation on Manifolds With Conical Singularities

Communications in Partial Differential Equations, 2016
Nikolaos Roidos, Elmar Schrohe
exaly  

Structural Stability for the Darcy Equations of Flow in Porous Media

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998
Brian Straughan, L E Payne
exaly  

The porous medium equation

1986
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