论文标题
全球解决方案，用于具有退化系数和时间加权来源的耦合抛物线系统
Global solution for a coupled parabolic system with degenerate coefficients and time-weighted sources
论文作者
论文摘要
在本文中，我们将所谓的Fujita指数带到以下抛物线系统，并具有时间加权的来源和退化系数$ u_ {t} - \ mbox {div}（ω（x）\ nabla \ nabla {u} ω（x）\ nabla {v}）= t^{s} u^{p} $ in $ \ mathbb {r}^{n}^{n}^{n} \ times（0，t）$，具有属于$ \ left [l^\ infty [l^\ infty（\ mathbb {\ mathb {r}^n）\ right] $ right的初始数据。 $ r，s> -1 $;和$ω（x）= | x_1 |^{a}，$或$ω（x）= | x |^{b} $带有$ a，b> 0 $。
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 $a,b > 0$.
