## Abstract

We study a blow-up curve for the one dimensional wave equation ∂^{2}_{t}u - ∂^{2}_{x}u = |∂_{t}u|^{p} with p > 1. The purpose of this paper is to show that the blow-up curve is a C1 curve if the initial values are large and smooth enough. To prove the result, we convert the equation into a first order system, and then apply a modification of the method of Caffarelli and Friedman [2]. Moreover, we present some numerical investigations of the blow-up curves. From the numerical results, we were able to confirm that the blow-up curves are smooth if the initial values are large and smooth enough. Moreover, we can predict that the blow-up curves have singular points if the initial values are not large enough even they are smooth enough.

Original language | English |
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Pages (from-to) | 373-408 |

Number of pages | 36 |

Journal | Advances in Differential Equations |

Volume | 23 |

Issue number | 5-6 |

Publication status | Published - 2018 May 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics