The blow-up curve of solutions to one dimensional nonlinear wave equations with the Dirichlet boundary conditions

Tetsuya Ishiwata, Takiko Sasaki

Research output: Contribution to journalArticle

Abstract

In this paper, we consider the blow-up curve of semilinear wave equations. Merle and Zaag (Am J Math 134:581–648, 2012) considered the blow-up curve for ∂t2u-∂x2u=|u|p-1u and showed that there is the case that the blow-up curve is not differentiable at some points when the initial value changes its sign. Their analysis depends on the variational structure of the problem. In this paper, we consider the blow-up curve for ∂t2u-∂x2u=|∂tu|p-1∂tu which does not have the variational structure. Nevertheless, we prove that the blow-up curve is not differentiable if the initial data changes its sign and satisfies some conditions.

Original languageEnglish
JournalJapan Journal of Industrial and Applied Mathematics
DOIs
Publication statusAccepted/In press - 2019 Jan 1

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Wave equations
Boundary conditions

Keywords

  • Blow-up
  • Positive solutions
  • Wave equation

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

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