Large time behavior of solutions to a class of doubly nonlinear parabolic equations. (English) Zbl 0787.35047

Manfredi, Juan J.; Vespri, Vincenzo

Electron. J. Differ. Equ. 1994, No. 02, 17 p. (1994).

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

Reviewer: J.J.Manfredi (Pittsburgh)

MSC:

35K65	Degenerate parabolic equations
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

large time asymptotic behavior; doubly degenerate parabolic equation; bounded domain