Uniform blow-up profiles and boundary layer for a parabolic system with localized sources

This paper deals with the Dirichlet problem for a parabolic system with localized sources. We first obtain some sufficient conditions for blow-up in finite time, and then deal with the possibilities of simultaneous blow-up under suitable assumptions. Moreover, when simultaneous blow-up occurs, we also establish the uniform blow-up profiles in the interior and estimate the boundary layer.