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Regularity of the blow-up curve at characteristic points for nonlinear wave equations

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Abstract

In this paper, we study a blow-up curve for one dimensional nonlinear wave equation of derivative type. We prove that the blow-up curve is a continuously differentiable function under suitable condition. Moreover, we show that the derivative of the blow-up curve is equivalent to the propagation velocity of the wave equation at a point.

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Authors and Affiliations

  1. National Institute of Technology (KOSEN), Ibaraki College, Hitachinaka, Ibaraki, 312-8508, Japan

    Takiko Sasaki

  2. Mathematical Institute, Tohoku University Aoba, Sendai, 980-8578, Japan

    Takiko Sasaki

  3. Graduate School of Engineering, Musashino University, Kotoku, Tokyo, 135-8181, Japan

    Takiko Sasaki

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  1. Takiko Sasaki
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Correspondence to Takiko Sasaki.

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Sasaki, T. Regularity of the blow-up curve at characteristic points for nonlinear wave equations. Japan J. Indust. Appl. Math. 39, 1055–1073 (2022). https://doi.org/10.1007/s13160-022-00548-5

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  • DOI: https://doi.org/10.1007/s13160-022-00548-5

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