Kerun Shao, Hiroyuki Takamura, Chengbo Wang
Published 2024-06-04Version 1
For small-amplitude semilinear wave equations with power type nonlinearity on the first-order spatial derivative, the expected sharp upper bound on the lifespan of solutions is obtained for both critical cases and subcritical cases, for all spatial dimensions $n>1$. It is achieved uniformly by constructing the integral equations, deriving the ordinary differential inequality system, and iteration argument. Combined with the former works, the sharp lifespan estimates for this problem are completely established, at least for the spherical symmetric case.
Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds
The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative
On the critical exponent and sharp lifespan estimates for semilinear damped wave equations with data from Sobolev spaces of negative order
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