Global existence for the 3-D semilinear damped wave equations in the scattering case

TL;DR

This paper proves the global existence of solutions for 3-D semilinear damped wave equations with derivative nonlinearities on certain geometric manifolds, using energy estimates and local existence techniques.

Contribution

It introduces a method to handle the scattering case on asymptotically Euclidean manifolds by converting the damping parameter to a small value.

Findings

Established global existence under specified conditions.

Utilized local energy estimates and local existence theory.

Extended results to nontrapping asymptotically Euclidean manifolds.

Abstract

We study the global existence of solutions to semilinear damped wave equations in the scattering case with derivative power-type nonlinearity on (1+3) dimensional nontrapping asymptotically Euclidean manifolds. The main idea is to exploit local energy estimate, together with local existence to convert the parameter $\mu$ to small one.