The critical exponent for a weakly coupled system of the generalized Fujita type reaction-diffusion equations (Q1894286)

This article is concerned with the system \[ u_t= L_1 u+ t^{S_1} v^{p_1},\;v_t= L_2 v+ t^{S_2} u^{p_2},\quad (x,t)\in \mathbb{R}^N\times (0, T) \] with given nonnegative initial values. It is assumed that \(S_1, S_2\geq 0\), \(p_1, p_2\geq 1\) and \(p_1, p_2> 1\). \(L_1\), \(L_2\) are uniformly elliptic operators whose coefficients are independent of \(t\). The author proves local existence and global nonexistence results.