The Behavior of Solutions for Equation of Filtration with Nonlinear Reaction-Convection

Abstract

This paper Presentsdescription of behavior of local solutions near the interface in the irregular domain in astate slow diffution. Therefore it appears  the different types of interface  as a result, the interfaces may expand, shrink or remain stationary relying on the competition between these factors.Also,it is researched  the attention is initial develop of interface and structure of a non negative weak solution. In our proof, the rescaling method and blow-up techniques are applied.