Non-simultaneous blow-up in parabolic equations coupled via localized sources

This work deals with non-simultaneous and simultaneous blow-up solutions for ut=Δu+um(x0,t)vp(x0,t), vt=Δv+uq(x0,t)vn(x0,t), subject to homogeneous Dirichlet boundary conditions. We obtain the complete results of non-simultaneous and simultaneous blow-up solutions for any fixed point x0 in any general bounded domain. The critical exponents of non-simultaneous blow-up are proposed.