Riemann type initial boundary value problem for a system in elastodynamics

TL;DR

This paper extends previous work on elastodynamics initial boundary value problems by considering general Riemann type data, formulating the problem based on Riemann problems, and explicitly constructing solutions.

Contribution

It introduces a new approach for solving elastodynamics boundary value problems with general Riemann type data, expanding beyond previous invariant-level set assumptions.

Findings

Explicit solutions for the Riemann type boundary value problem in elastodynamics

Generalization of initial and boundary data beyond invariant level sets

Formulation of the boundary value problem based on Riemann problems

Abstract

This paper is a continuation of our previous paper \cite{d1} on the initial boundary value problem for a nonconservative system appearing in elastodynamics in the space time domain $x>0,t>0$. There, the initial and boundary data were assumed to lie on the level sets of one of the Riemann invariants where as in this paper we consider the general initial and boundary data of Riemann type, formulate the boundary value problem based on the Riemann problem and construct explicitly the solution.