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arXiv · 2605.07487

Gradient Catastrophe for Solutions to the Conservation Laws with Source Term

Qingsong Zhao
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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.

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Qingsong Zhao. 2026-05-08. Gradient Catastrophe for Solutions to the Conservation Laws with Source Term. https://arxiv.org/abs/2605.07487

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