Asymptotic method of moving planes for fractional parabolic equations

By Wenxiong CHEN *, Pengyan Wang, Yahui Niu, Yunyun Hu. 2020

55 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/169833b7de055da2ee17980a8b77d94f8ff1b50a

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In Applied Mathematics

1. Leyun Wu
2. Wenxiong CHEN *
3. Congming LI #
4. Li Ma
5. Yutian Lei
6. L. Martinazzi
7. Fengbo Hang
8. Dezhong Chen

In Computational Theory and Mathematics

1. Leyun Wu
2. Wenxiong CHEN *
3. Congming LI #

Citations in the corpus

• Liouville Theorems for Fractional Parabolic Equations (2021, background): “In previous literature, for instance in [13], to establish a narrow region principle in an unbounded domain, one usually assumed that lim |x|→+∞ wλ(x, t) = 0.”