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

  • Ataru Fujii

    University of Tokyo, Japan
  • Masahito Ohta

    University of Tokyo, Japan

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