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 . 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.
|Number of pages||36|
|Journal||Advances in Differential Equations|
|Publication status||Published - 2018 May 1|
ASJC Scopus subject areas
- Applied Mathematics