On the long-time behaviour of solutions of the $p$-Laplacian parabolicsystem
Volume 113 / 2008
Colloquium Mathematicum 113 (2008), 267-278
MSC: Primary 35B40; Secondary 35K65.
DOI: 10.4064/cm113-2-8
Abstract
Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the $p$-Laplacian operator is proved. A similar result is obtained for a variable exponent $p$. In the case of $p$ constant, the convergence is proved to be ${\mathcal{C}}^1_{\rm loc}$, and in the variable exponent case, $L^2$ and $W^{1,p(x)}$-weak.
