Existence of solutions to the Rosenau and Benjamin-Bona-Mahony equation in domains with moving boundary

Abstract

In this article, we prove the existence of solutions for a hyperbolic equation known as the the Rosenau and Benjamin-Bona-Mahony equations. We study increasing, decreasing, and mixed non-cylindrical domains. Our main tools are the Galerkin method, multiplier techniques, and energy estimates.