Time-weighted blow-up profiles in a nonlinear parabolic system with Fujita exponent

In this paper, we deal with a time-weighted parabolic system coupled via nonlocal sources. Firstly, we give the critical Fujita exponent of solutions. Secondly, we propose the time-weighted blow-up profiles of solutions. Thirdly, the simultaneous and non-simultaneous blow-up of solutions are discussed under some conditions on the initial data. Fourthly, besides blow-up rates, we classify total blow-up and single point blow-up of solutions. At last, upper and lower bounds of blow-up time are studied according to precise blow-up phenomena.