Global stability in a nonlocal reaction-diffusion equation

Finkelshtein D, Kondratiev Y, Molchanov S, Tkachov P (2018)
STOCHASTICS AND DYNAMICS 18(5): 1850037.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Finkelshtein, Dmitri; Kondratiev, YuriUniBi; Molchanov, Stanislav; Tkachov, Pasha
Abstract / Bemerkung
We study stability of stationary solutions for a class of nonlocal semilinear parabolic equations. To this end, we prove the Feynman-Kac formula for a Levy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the zero solution, and use them to the study of the spatial logistic equation arising in population ecology. For this equation, we find conditions which imply that its positive stationary solution is asymptotically stable. We consider also the case when the initial condition is given by a random field.
Stichworte
Nonlocal diffusion; Feynman-Kac formula; Levy processes; reaction-diffusion equation; semilinear parabolic equation; monostable; equation; nonlocal nonlinearity
Erscheinungsjahr
2018
Zeitschriftentitel
STOCHASTICS AND DYNAMICS
Band
18
Ausgabe
5
Art.-Nr.
1850037
ISSN
0219-4937
eISSN
1793-6799
Page URI
https://pub.uni-bielefeld.de/record/2931493

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Finkelshtein D, Kondratiev Y, Molchanov S, Tkachov P. Global stability in a nonlocal reaction-diffusion equation. STOCHASTICS AND DYNAMICS. 2018;18(5): 1850037.
Finkelshtein, D., Kondratiev, Y., Molchanov, S., & Tkachov, P. (2018). Global stability in a nonlocal reaction-diffusion equation. STOCHASTICS AND DYNAMICS, 18(5), 1850037. doi:10.1142/S0219493718500375
Finkelshtein, D., Kondratiev, Y., Molchanov, S., and Tkachov, P. (2018). Global stability in a nonlocal reaction-diffusion equation. STOCHASTICS AND DYNAMICS 18:1850037.
Finkelshtein, D., et al., 2018. Global stability in a nonlocal reaction-diffusion equation. STOCHASTICS AND DYNAMICS, 18(5): 1850037.
D. Finkelshtein, et al., “Global stability in a nonlocal reaction-diffusion equation”, STOCHASTICS AND DYNAMICS, vol. 18, 2018, : 1850037.
Finkelshtein, D., Kondratiev, Y., Molchanov, S., Tkachov, P.: Global stability in a nonlocal reaction-diffusion equation. STOCHASTICS AND DYNAMICS. 18, : 1850037 (2018).
Finkelshtein, Dmitri, Kondratiev, Yuri, Molchanov, Stanislav, and Tkachov, Pasha. “Global stability in a nonlocal reaction-diffusion equation”. STOCHASTICS AND DYNAMICS 18.5 (2018): 1850037.