On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source

TL;DR

This paper investigates the well-posedness and regularity of solutions for a wave equation with hyperbolic dynamical boundary conditions, damping, and sources, establishing a dynamical system under certain source conditions.

Contribution

It provides new results on local Hadamard well-posedness and solution regularity for wave equations with complex boundary conditions and damping, including the generation of a dynamical system.

Findings

Established local Hadamard well-posedness.

Analyzed regularity of solutions.

Generated a dynamical system under specific source conditions.

Abstract

The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for initial data in the natural energy space. Moreover the regularity of solutions is studied. Finally a dynamical system is generated when sources are at most linear at infinity, or they are dominated by the damping terms.