Uniform blow-up profiles for heat equations with coupling nonlocal sources of asymmetric mixed type nonlinearities

This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions, where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities. We at first give the criterion for simultaneous blow-up of solutions, and then establish the uniform blow-up profiles of solutions near the blow-up time. It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmetric, but also the blow-up rates of the same component u (or v) may be in different levels under different dominations.