Gradient Catastrophe for Solutions to the Conservation Laws with Source Term
Analysis of PDEs
2026-05-12 v1
Abstract
This paper studies singularity formation for conservation laws with a source term. Motivated by John (1974) and Barlin (2023), we prove finite-time blow-up under initial data conditions weaker than those in Barlin. Moreover, we show that a sufficiently small compact support length of the initial data promotes blow-up. Hence, global existence can only be achieved when the initial data have a large compact support length.
Cite
@article{arxiv.2605.07487,
title = {Gradient Catastrophe for Solutions to the Conservation Laws with Source Term},
author = {Qingsong Zhao},
journal= {arXiv preprint arXiv:2605.07487},
year = {2026}
}