Blow-up of solutions to a scalar conservation law with nonlocal source arising in radiative gas

Abstract

In this paper we consider a scalar conservation law with nonlocal source arising in radiative gas. We give a sufficient condition to assure that the solution blows up in a finite time. Moreover, the estimates of life span and blow-up rate are derived.

Keywords:

• Blow-up
• nonlocal source
• scalar conservation law
• radiative gas

Mathematics Subject Classifications:

• 35L65
• 35B30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

No data was used for the research described in the article.

Additional information

Funding

This work is supported by Yunnan Fundamental Research Projects (Grant NO. 202101BE070001-050).