Electronic Journal of Differential Equations,
Vol. 1994(1994), No. 02, pp. 1-17. Published March 15, 1994.
Title: Large Time Behavior of Solutions to a Class of Doubly
Nonlinear Parabolic Equations
Authors: Juan J. Manfredi (Univ. of Pittsburgh, PA, USA)
Vincenzo Vespri (Univ. di Pavia, Italy)
Abstract: 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 $m+p\geq 3$, $p>1$, and the
initial datum $u_0$ is in $L^1(\Omega)$.
Submitted October 25, 1993. Published March 15, 1994.
Math Subject Classification: 35K65, 35K55.
Key Words: Doubly nonlinear parabolic equations; asymptotic behavior.