Publications of the Research Institute for Mathematical Sciences


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Volume 32, Issue 3, 1996, pp. 503–515
DOI: 10.2977/prims/1195162854

Published online: 1996-06-30

Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the p-Laplacian

Ataru Fujii and Masahito Ohta

We consider the blowup problem for ut = Δpu + ∣ up–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.

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Fujii Ataru, Ohta Masahito: Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the p-Laplacian. Publ. Res. Inst. Math. Sci. 32 (1996), 503-515. doi: 10.2977/prims/1195162854