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Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations
Takiko Sasaki, Kerun Shao, Hiroyuki Takamura
This paper is devoted to a simple and short proof on the sharp upper bound of lifespan of classical solutions to wave equations with the critical power nonlinearities of spatial de…
Criteria of the existence of global solutions to semilinear wave equations with first-order derivatives on exterior domains
Kerun Shao
We study the existence of global solutions to semilinear wave equations on exterior domains , , with small initial data and nonlinear term…
Blow-up of solutions to semilinear wave equations with spatial derivatives
Kerun Shao, Hiroyuki Takamura, Chengbo Wang
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 obt…
Global Solutions with Small Initial Data to Semilinear Wave Equations with Energy Supercritical Powers
Kerun Shao, Chengbo Wang
Considering dimensional semilinear wave equations with energy supercritical powers , we obtain global solutions for any initial data with small norm in $H^{s_c}…