Abstract
We study a blow-up curve for the one dimensional wave equation ∂2tu - ∂2xu = |∂tu|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