Generalized solution of a mixed problem for linear hyperbolic system

TL;DR

This paper establishes existence and uniqueness of generalized solutions for a linear hyperbolic system's mixed problem within Colombeau algebra and applies it to wave propagation in discontinuous media.

Contribution

It introduces a novel existence-uniqueness framework for hyperbolic systems in Colombeau algebra and demonstrates its application to complex wave propagation scenarios.

Findings

Proved existence and uniqueness of solutions in Colombeau algebra.

Applied the theoretical results to wave propagation in discontinuous environments.

Validated the approach through specific problem examples.

Abstract

In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave propagation problem in a discontinuous environment.