Cauchy problem for nonlocal diffusion equations modelling Lévy flights

Sin Chung-Sik: Cauchy problem for nonlocal diffusion equations modelling Lévy flights. (2022)

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In the present paper, we study the time-space fractional diffusion equation involving the Caputo differential operator and the fractional Laplacian. This equation describes the Lévy flight with the Brownian motion component and the drift component. First, the asymptotic behavior of the fundamental solution of the fractional diffusion equation is considered. Then, we use the fundamental solution to obtain the representation formula of solutions of the Cauchy problem. In the last, the L 2 -decay estimates for solutions are proved by employing the Fourier analysis technique.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 18
ISSN: 1417-3875
Number of Pages: 22
Language: English
Place of Publication: Szeged
DOI: 10.14232/ejqtde.2022.1.18
Uncontrolled Keywords: Differenciáloperátor, Differenciálegyenlet
Additional Information: Bibliogr.: p. 20-22. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. May. 24. 08:45
Last Modified: 2022. May. 24. 08:45

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