Note on a parabolic problem with multi-coupled nonlinearity and space-time weighted functions

Abstract

This paper deals with two semilinear parabolic equations involving multi-coupled nonlinearity, where the weighted functions depend on space and time variables. We determine the exponent regions where the nonnegative nontrivial solutions blow up for any initial data. Moreover, some exponent regions on the global solutions are given with some conditions on the initial data and the ten exponents.