Special Session 131: Recent progress on singularities formations of some evolution partial differential equations

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

Takiko Sasaki
Musashino Unversity
Japan
Co-Author(s):    Shu Takamatsu, Hiroyuki Takamura
Abstract:
This talk 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 timederivative. 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.