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

Mengyun Liu, Chengbo Wang

Published 2018-07-16Version 1

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.