A Class of Evolutionary Problems with an Application to Acoustic Waves with Impedance Type Boundary Conditions

TL;DR

This paper studies a class of evolutionary operator equations with applications to acoustic wave equations involving complex materials, impedance boundary conditions, and effects like memory and delay, providing a comprehensive mathematical framework.

Contribution

It introduces a new class of evolutionary problems incorporating memory and delay effects with impedance boundary conditions, advancing the mathematical modeling of acoustic waves.

Findings

Established well-posedness of the operator equations

Extended the model to include complex material laws and boundary effects

Provided a framework for analyzing acoustic waves with memory and delay

Abstract

A class of evolutionary operator equations is studied. As an application the equations of linear acoustics are considered with complex material laws. A dynamic boundary condition is imposed which in the time-harmonic case corresponds to an impedance or Robin boundary condition. Memory and delay effects in the interior and also on the boundary are built into the problem class.