The limit of vanishing viscosity for doubly nonlinear parabolic equations
We show that solutions of the doubly nonlinear parabolic equation \begin{equation*} \frac{\partial b(u)}{\partial t} - \epsilon \operatorname{div}(a(\nabla u)) + \operatorname{div}(f(u)) = g \end{equation*} converge in the limit $\epsilon \searrow 0$ of vanishing viscosity to an entropy so...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
University of Szeged
2014-03-01
|
Series: | Electronic Journal of Qualitative Theory of Differential Equations |
Subjects: | |
Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=2470 |
Summary: | We show that solutions of the doubly nonlinear parabolic equation
\begin{equation*}
\frac{\partial b(u)}{\partial t} - \epsilon \operatorname{div}(a(\nabla u)) + \operatorname{div}(f(u)) = g
\end{equation*}
converge in the limit $\epsilon \searrow 0$ of vanishing viscosity to an entropy solution of the doubly nonlinear hyperbolic equation
\begin{equation*}
\frac{\partial b(u)}{\partial t} + \operatorname{div}(f(u)) = g \,.
\end{equation*}
The difficulty here lies in the fact that the functions $a$ and $b$ specifying the diffusion are nonlinear. |
---|---|
ISSN: | 1417-3875 |