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

Abstract

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 $\omega (x)=|x_1{|}^a,$ or $\omega (x)=|x{|}^b$ with $a,b>0$.