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Title: Topics in fractional Laplacian and dynamical systems
Authors: Chen, Wenxiong
Nandori, Peter
Gidea, Marian
Marini, Antonella
Catrina, Florin
Liu, Xingyu
Keywords: Fractional Laplacian
Dynamical system
Fractional parabolic equation
Lorentz Gas
Parabolic Monge-Ampere equations
Issue Date: Jun-2023
Publisher: Yeshiva University
Citation: Liu, X. (2023, June). Topics in fractional Laplacian and dynamical systems (Publication No. 30567473) [Doctoral dissertation, Yeshiva University]. PDTG
Series/Report no.: Katz Doctoral Dissertations;Publication No. 30567473
Abstract: Abstract In this thesis, we consider problems involving the $n$-dimensional fractional Laplacians including elliptic equations and parabolic equations. We also consider the problems involving fractional Monge-Amp\'ere operators. The thesis is mostly devoted to presenting our original work on the progress obtained in the development of direct methods that can effectively deal with the above problems. ¶ In the second part of the work, we are interested in the length of a few consecutive long free flights in infinite horizon Lorentz Gas. In dimension D=2, it is well known that a flight of length T>>1 is typically followed by a flight of length $C\sqrt{T}$. Here, we extend this result to any dimension $D$.
Description: Doctoral dissertation, PhD / Open Access
Appears in Collections:Mathematical Sciences Dissertations

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