arXiv:2306.07070 Abstract | arXiv Analytics

arXiv:2306.07070 [math.AP]Abstract References Reviews Resources

The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative

Takiko Sasaki, Shu Takamatsu, Hiroyuki Takamura

Published 2023-06-12Version 1

This paper is devoted to the lifespan estimates of small classical solutions of the initial value problems for one dimensional wave equations with semilinear terms of the spatial derivative of the unknown function. It is natural that the result is same as the one for semilinear terms of the time-derivative. But there are so many differences among their proofs. Moreover, it is meaningful to study this problem in the sense that it may help us to investigate its blow-up boundary in the near future.

Comments: 10 pages

Categories: math.AP

Subjects: 35L71, 35B44

Keywords: dimensional wave equations, semilinear terms, spatial derivative, initial value problems, lifespan estimates

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