Global existence for semilinear damped wave equations in relation with the Strauss conjecture

2018/07/16 by Liu, Mengyun, Wang, Chengbo · 1 citation
#35B33 #35L05 #35L15 #35L71 #58J45 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.05908

Abstract

We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on n dimensional nontrapping asymptotically Euclidean manifolds, when n=3, 4. In addition, we prove almost global existence with sharp lower bound of the lifespan for the four dimensional critical problem.

Cited by

• On the blow-up of solutions to a Nakao-type problem with a time-dependent damping term

Related

• Global existence for the 3-D semilinear damped wave equations in the scattering case
• Lifespan estimates for wave equations with damping and potential posed on asymptotically Euclidean manifolds
• Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds
• Global existence for a coupled wave system related to the Strauss\n conjecture
• Global existence and blow-up for semilinear damped wave equations in three space dimensions