论文标题
分数抛物线方程移动平面的渐近方法
Asymptotic method of moving planes for fractional parabolic equations
论文作者
论文摘要
在本文中，我们开发了一种系统的方法，用于应用一种渐近方法来研究分数抛物线方程的阳性溶液的定性特性。我们首先获得一系列所需的关键成分，例如狭窄的区域原理，以及在有限和无界域中的反对称函数的各种渐近最大和强最大原理。然后，我们说明如何使用这种新方法来获得单位球和整个空间中阳性溶液的渐近径向对称性和单调性。也就是说，我们表明，无论最初的数据是什么，解决方案最终都将接近径向对称函数。 我们坚信，此处介绍的思想和方法可以方便地用于研究各种普通运营商和更一般的非线性的非局部抛物线问题。
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key ingredients such as narrow region principles, and various asymptotic maximum and strong maximum principles for antisymmetric functions in both bounded and unbounded domains. Then we illustrate how this new method can be employed to obtain asymptotic radial symmetry and monotonicity of positive solutions in a unit ball and on the whole space. Namely, we show that no matter what the initial data are, the solutions will eventually approach to radially symmetric functions. We firmly believe that the ideas and methods introduced here can be conveniently applied to study a variety of nonlocal parabolic problems with more general operators and more general nonlinearities.
