Semilinear wave equations with time-dependent coefficients

TL;DR

This paper establishes the existence and uniqueness of solutions for semilinear wave equations with time- and space-dependent coefficients, providing theoretical results and practical examples.

Contribution

It introduces new existence and uniqueness results for semilinear wave equations with variable coefficients, extending previous work to more general settings.

Findings

Existence of strong and weak solutions proven

Uniqueness established under additional assumptions

Abstract results illustrated with practical examples

Abstract

We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under slightly more restrictive assumptions. Furthermore, the results obtained in abstract setting are illustrated on practical examples.