On General Balance Laws with Boundary

TL;DR

This paper studies general balance laws with non-local sources and non-characteristic boundaries, establishing well-posedness, sharp estimates, and new uniqueness results, especially highlighting boundary characteristic effects.

Contribution

It provides new well-posedness results, sharp boundary estimates, and uniqueness theorems for balance laws with non-local sources and boundaries.

Findings

Bounds blow up as boundary approaches characteristic

Established sharp estimates for solutions

Proved new uniqueness results for boundary value problems

Abstract

This paper is devoted to general balance laws (with a possibly non local source term) with a non-characteristic boundary. Basic well posedness results are obtained, trying to provide sharp estimates. In particular, bounds tend to blow up as the boundary tends to be characteristic. New uniqueness results for the solutions to conservation and/or balance laws with boundary are also provided.