# Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters

## TL;DR

This paper investigates wave propagation in media with irregular dissipation, introducing a very weak solution framework and demonstrating phenomena like echo effects at discontinuities through numerical simulations.

## Contribution

It develops a theoretical approach for dissipative wave equations with distributional dissipation and explores novel wave phenomena at medium discontinuities.

## Key findings

- Existence of very weak solutions for dissipative wave equations
- Numerical evidence of a new wave phenomenon at discontinuities
- Identification of echo effects in acoustic problems

## Abstract

In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show that this problem has a so-called very weak solution, we analyse its properties and illustrate the theoretical results through some numerical simulations by approximating the solutions to the full dissipative model for a particular synthetic piecewise continuous medium. In particular, we discover numerically a very interesting phenomenon of the appearance of a new wave at the singular point. For the acoustic problem this can be interpreted as an echo effect at the discontinuity interface of the medium.