The existence of continuous weak solutions with compact support for degenerate parabolic systems with exchange-type source

Abstract

The presence of exchange-type source is an important feature of the radiation diffusion model coupled with material heat transfer. In this paper, we prove the existence of continuous weak solutions with compact support for the Cauchy problem of two classes of degenerate diffusion systems with exchange-type sources. One class is weakly coupled and another is special strongly coupled. For special strongly coupled degenerate systems, we further prove that the support of radiation is concurrent with that of material temperature, and the supports are extending as time goes on, which can be derived as a consequence of the exchange mechanism.

Keywords:

• Degenerate parabolic systems
• compact support
• exchange-type sources

AMS:

• 35B60
• 35K10
• 35K57
• 35K65

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (12126307 and 11971069).