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

In this paper, we obtain the so-called Fujita exponent to the following parabolic system with time-weighted sources and degenerate coefficients $ u_{t}- \mbox{div} ( ω(x)\nabla { u} )= t^{r} v^{p} $ and $ v_{t}- \mbox{div} ( ω(x)\nabla {v} )= t^{s} u^{p}$ in $\mathbb{R}^{N} \times (0,T)$ with initial data belonging to $\left[L^\infty(\mathbb{R}^N)\right]^2.$ Where $p,q > 0$ with $pq > 1$; $r,s>-1$; and either $ω(x) = | x_1|^{a},$ or $ω(x) = | x |^{b}$ with $a,b > 0$.

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