Asymptotic behavior of blowup solutions of a parabolic equation with the p-laplacian

Ataru Fujii, Masahito Ohta

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We consider the blowup problem for ut = Δpu + |u|p-2u (x ∈ Ω , t > 0) under the Dirichlet boundary condition and p > 2. We derive sufficient conditions on blowing up of solutions. In particular, it is shown that every non-negative and non-zero solution blows up in a finite time if the domain Ω is large enough. Moreover, we show that every blowup solution behaves asymptotically like a self-similar solution near the blowup time. The Rayleigh type quotient introduced in Lemma A plays an important role throughout this paper.

Original languageEnglish
Pages (from-to)503-515
Number of pages13
JournalPublications of the Research Institute for Mathematical Sciences
Volume32
Issue number3
DOIs
Publication statusPublished - Oct 1996

    Fingerprint

Cite this