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

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. [ABSTRACT FROM AUTHOR]