Porous medium equation and fast diffusion equation as gradient systems

Czechoslovak Mathematical Journal

Samuel Littig¹ 

[1] Jrgen Voigt, TU Dresden, Fachrichtung Mathematik, Helmholtzstrasse10, D-01062 Dresden, Germany

关键词: porous medium equation;    gradient system;    fast diffusion;    asymptotic behaviour;    order preservation;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

We show that the Porous Medium Equation and the Fast Diffusion Equation, $\dot u-\Delta u^m=f$, with $m\in(0,\infty)$, can be modeled as a gradient system in the Hilbert space $H^{-1}(\Omega)$, and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets $\Omega\subseteq\mathbb R^n$ and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions.

【 授权许可】

Unknown