Relaxation approximation of Friedrich's systems under convex constraints

TL;DR

This paper introduces a relaxation method for Friedrichs' systems with convex constraints, proving strong convergence of the approximation to the unique solution in a local L^2 sense.

Contribution

It presents a new relaxation approximation approach for Friedrichs' systems under convex constraints, with a rigorous convergence proof.

Findings

Strong convergence of the approximation in L^2_{loc}

Unique constrained solution exists and is approximated effectively

Method applicable to a class of Friedrichs' systems

Abstract

This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in L^2\_{loc} of a parabolic-relaxed approximation towards the unique constrained solution.