论文标题
全球解决方案的存在和不存在，具有退化系数的热方程
Existence and non-existence of global solutions for a heat equation with degenerate coefficients
论文作者
论文摘要
在本文中，我们将研究以下抛物面问题$ u_t -div（ω（x）\ nabla u）= h（t）f（t）f（t）f（u） + l（t）g（u）g（u）$，具有与$ c_b（\ mathbb {rsbb {r}^n）$的$ c_b（\ mathbb {r}^n）$的非负初始条件，其重量$ $ $ aunc属于$ ungs。 \ frac {2} {n}} $和功能$ f $，$ g $，$ h $和$ l $是非负和连续的。主要目标是建立非负解决方案的全球和非全球存在。此外，要介绍特定情况时，当$ h（t）\ sim t^r ~~（r> -1）$，$ l（t）\ sim t^s ~~（s> -1）$，$ f（u）= u^p $和$ g（u^p $ and $ g（u）=（u）=（u）=（1+u）[\ ln（1+u）] ni \ cite {lee-ni}。我们的结果扩展了Fujishima等人获得的结果。 \ cite {fujish}谁在$ h（t）= 1 $，$ l（t）= 0 $和$ f（u）= u^p $时工作。
In this paper, we will study the following parabolic problem $u_t - div(ω(x) \nabla u)= h(t) f(u) + l(t) g(u)$ with non-negative initial conditions pertaining to $C_b(\mathbb{R}^N)$, where the weight $ω$ is an appropriate function that belongs to the Munckenhoupt class $A_{1 + \frac{2}{N}}$ and the functions $f$, $g$, $h$ and $l$ are non-negative and continuous. The main goal is to establish of global and non-global existence of non-negative solutions. In addition, to present the particular case when $h(t) \sim t^r ~~ (r>-1)$, $l(t) \sim t^s ~~ (s>-1)$, $f(u) = u^p$ and $g(u)= (1+u)[\ln(1+u)]^p,$ we obtain both the so-called Fujita's exponent and the second critical exponent in the sense of Lee and Ni \cite{Lee-Ni}. Our results extend those obtained by Fujishima et al. \cite{Fujish} who worked when $h(t)=1$, $l(t)=0$ and $f(u)=u^p $.
