Large time behavior of solution to a class of doubly nonlinear parabolic equations

Abstract

solutions of the doubly degenerate parabolic equation $u_t={ m div} (|u|^{m-1}|abla u|^{p-2}abla u)$ in a cylinder $Omegaimes R^+$, with initial condition $u(x,0)=u_0(x)$ in $Omega$ and vanishing on the parabolic boundary $partialOmegaimes R^+$. Here $Omega$ is a bounded domain in $R^N$, the exponents $m$ and $p$ satisfy $m+pgeq 3$, $p>1$, and the initial datum $u_0$ is in $L^1(Omega)$.

Keywords

• Doubly nonlinear parabolic equations
• asymptotic behavior.