论文标题
两种类型的快速扩散方程的大时渐近行为
Large Time Asymptotic Behaviors of Two Types of Fast Diffusion Equations
论文作者
论文摘要
我们考虑在r^n中的两种类型的非线性快速扩散方程：（1）具有一般外部电位的外部漂移类型方程。这是谐波潜在案例的自然扩展，在许多论文中都对此进行了研究。在本文中，我们可以使用熵方法证明对固定状态的近时间渐近行为。（2）带有卷积项的平均场类型方程。固定溶液是自由能函数的最小化器，该功能与反向强硬的小木 - 贝贝列夫不等式直接关系。在本文中，我们证明在某些特殊情况下，它也存在于固定状态的大渐近行为。
We consider two types of non linear fast diffusion equations in R^N:(1) External drift type equation with general external potential. It is a natural extension of the harmonic potential case, which has been studied in many papers. In this paper we can prove the large time asymptotic behavior to the stationary state by using entropy methods.(2) Mean-field type equation with the convolution term. The stationary solution is the minimizer of the free energy functional, which has direct relation with reverse Hardy-Littlewood-Sobolev inequalities. In this paper, we prove that for some special cases, it also exists large time asymptotic behavior to the stationary state.
