Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the -Laplacian
Ataru Fujii
University of Tokyo, JapanMasahito Ohta
University of Tokyo, Japan
![Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the $p$-Laplacian cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-prims-volume-32-issue-3.png&w=3840&q=90)
Abstract
We consider the blowup problem for (, ) under the Dirichlet boundary condition and . 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 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.
Cite this article
Ataru Fujii, Masahito Ohta, Asymptotic Behavior of Blowup Solutions of a Parabolic Equation with the -Laplacian. Publ. Res. Inst. Math. Sci. 32 (1996), no. 3, pp. 503–515
DOI 10.2977/PRIMS/1195162854