Asymptotic results and critical Fujita exponent in parabolic equations with nonlocal nonlinearity

Abstract

This paper deals with the parabolic equations coupled via nonlocal multiple nonlinearity. We determine the critical Fujita exponents for blow-up solutions, which are influenced by the time coefficients. Moreover, we obtain the complete and optimal classification on simultaneous and non-simultaneous blow-up of solutions. Then simultaneous blow-up rates and estimates on blow-up time are studied according to the precise blow-up phenomena for all of the dimensions of the space domain.