Electron. J. Diff. Eqns., Vol. 1994(1994), No. 02, pp. 1-17. Published March 15, 1994.

Large Time Behavior of Solutions to a Class of Doubly Nonlinear Parabolic Equations

Juan J. Manfredi & Vincenzo Vespri

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 greater than 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.

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Juan J. Manfredi
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
e-mail: manfredi+@pitt.edu

Vincenzo Vespri Universita di Pavia, Dipartimento di Matematica, Via Abbiategrasso 209, 27100 Pavia, ITALY
e-mail: vespri@vmimat.mat.unimi.it

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