On the behavior of solutions of a doubly nonlinear degenerate parabolic system with nonlinear sources and absorptions with variable densities

In this paper, the problem of a doubly nonlinear degenerate parabolic system with nonlinear sources and absorption terms not located in a homogeneous medium was considered. It obeys zero Dirichlet boundary conditions in a smooth bounded domain. The comparison principle and self-similar approach was used to study the problem. In this paper, the nonlinear splitting method was used to prove the existence of global and blow-up in finite time solutions. It is shown that the role of the nonlinear source and nonlinear absorption is important for the existence and non-existence of the solution. The results contribute to a broader understanding of nonlinear parabolic systems.