论文标题
存在全球解决方案和用于分数扩散方程系统耦合系统的解决方案
Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations
论文作者
论文摘要
我们研究了一个半线性耦合的分数扩散方程系统的Cauchy问题，其多项式非线性在$％\ Mathbb {r} _ {+} \ times \ times \ Mathbb {r}^r}^{n} $中。在指数的适当条件和分数时间衍生物的顺序中，我们提出了尺寸n的临界值，该尺寸为n，为此存在较小数据的全球解决方案，否则解决方案在有限的时间内爆炸。此外，讨论了全球解决方案的庞大时间行为。
We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in $% \mathbb{R}_{+}\times \mathbb{R}^{N}$. Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed.
