Global solution for coupled parabolic systems with degenerate coefficients and time-weighted sources

In this article we obtained the so-called Fujita exponent for the degenerate parabolic coupled system $$\displaylines{ u_t- \text{div} ( \omega(x)\nabla u )= t^{r} v^{p} \cr v_t- \text{div} ( \omega(x)\nabla v )= t^{s} u^{p} }$$ in \(\mathbb{R}^{N} \times (0,T)\) with initial data belonging to \([ L^\infty(\mathbb{R}^N)]^2\), where \(p,q > 0\) with \(pq > 1\); \(r,s>-1\), and either \(\omega(x) = | x_1|^a\) or \(\omega(x) = | x |^b\) with \(a,b > 0\). For more information see https://ejde.math.txstate.edu/Volumes/2024/67/abstr.html