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

Tetsuya Ishiwata, Takiko Sasaki

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)339-363
ページ数25
ジャーナルJapan Journal of Industrial and Applied Mathematics
37
1
DOI
出版ステータスPublished - 2020 1月 1

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

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