Manfredi, Juan J.; Vespri, Vincenzo

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

Electron. J. Differ. Equ. 1994(2), (1994)


Summary: We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation $$u_t={\rm div} (|u|^{m-1}|\nabla u|^{p-2}\nabla u)$$ in a cylinder $\Omega\times R^+$, with initial condition $u(x,0)=u_0(x)$ in $\Omega$ and vanishing on the parabolic boundary $\partial\Omega\times R^+$. Here $\Omega$ is a bounded domain in $R^N$, the exponents m and p satisfy $m+p\geq 3, p greater than 1$, and the initial datum $u_0$ is in $L^1(\Omega)$.

Mathematics Subject Classification

35K65, 35K55


doubly nonlinear parabolic equations, asymptotic behavior