Blow-up for doubly degenerate parabolic system with nonlocal sources

Abstract

This article deals with the blow-up properties of the solution to a doubly degenerate parabolic system with nonlocal sources and inner absorptions, subject to homogeneous Dirichlet boundary conditions. We first establish the local existence and uniqueness of its classical solutions. Then we show that the critical exponent is determined by the interaction among all the six nonlinear exponents from all three kinds of the nonlinearities. Finally, we give the precise blow-up estimates and the uniform blow-up profiles.