Estimates for first-order homogeneous linear characteristic problems

TL;DR

This paper develops an algebraic criterion to establish a priori estimates for solutions of first-order homogeneous linear characteristic problems, ensuring their stability and well-posedness.

Contribution

It introduces a new algebraic criterion that guarantees the existence of stability estimates for these problems, enhancing understanding of their well-posedness.

Findings

Derived an algebraic criterion for stability estimates

Ensured solutions are stable under data variations

Identified conditions for well-posed characteristic problems

Abstract

An algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first-order homogeneous linear characteristic problems is derived. Estimates of such kind ensure the stability of the solutions under small variations of the data. Characteristic problems that satisfy this criterion are, in a sense, manifestly well posed.