Non-simultaneous blow-up in a semilinear parabolic system

Abstract.

In this paper we study the possibility of non-simultaneous blow-up for positive solutions of a fully coupled system of two semilinear heat equations, $u_t=\Delta u + u^{p_{11}} v^{p_{12}}, v_t=\Delta v + u^{p_{21}} v^{p_{22}}$. Under adequate hypotheses, we prove that if u blows up then v can fail to blow up if and only if $p_{11} >1$ and $p_{21} < p_{11}-1$.