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- Title
Some recent developments on fractional parabolic equations.
- Authors
Chen, Wenxiong; Dai, Wei; Guo, Yahong
- Abstract
In this paper, we provide a comprehensive overview of the recent developments in the field of fractional parabolic equations, with a primary focus on the underlying ideas and techniques. These results have appeared in a series of previous literatures, mainly in [30] [92] [29] [32] [97]. However, in these articles, the ideas were usually submerged in detailed calculations. What we are trying to do here is to highlight these ideas and illustrate the inner connections among them, so that the readers can see the whole picture and quickly grasp the essence of these useful methods and hence will be able to apply them to solve a variety of other problems in this area.Actually, many techniques and estimates in fractional elliptic equations can be modified and then be applied to investigate the corresponding parabolic fractional problems. We will clearly explain how to make such transitions in relevant sections.If you find it challenging to grasp the main ideas and essences of [30], [92], [29], [32], and [97], we suggest using this paper as a primer. Beginning with this work will provide you with a solid conceptual framework, making it much easier to navigate and comprehend the additional details in the aforementioned articles.
- Subjects
ELLIPTIC equations; EQUATIONS; ESTIMATION theory; LIOUVILLE'S theorem
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2024, Vol 44, Issue 9, p1
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2024044