Journal article 1210 views 172 downloads
Global stability in a nonlocal reaction-diffusion equation
Stochastics and Dynamics, Volume: 18, Issue: 05, Start page: 1850037
Swansea University Author:
Dmitri Finkelshtein
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DOI (Published version): 10.1142/S0219493718500375
Abstract
We study stability of stationary solutions for a class of nonlocal semi-linear parabolic equations. To this end, we prove a Feynman-Kac type formula for a Lévy processes with time-dependent potentials and arbitrary initial condition. We propose sufficient conditions for asymptotic stability of the z...
Published in: | Stochastics and Dynamics |
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ISSN: | 0219-4937 1793-6799 |
Published: |
World Scientific
2018
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Online Access: |
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URI: | https://cronfa.swan.ac.uk/Record/cronfa35092 |
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Abstract: |
We study stability of stationary solutions for a class of nonlocal semi-linear parabolic equations. To this end, we prove a Feynman-Kac type formula for a Lévy 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. |
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Keywords: |
Nonlocal diffusion; Feynman--Kac formula; L\'{e}vy processes; Reaction-diffusion equation; Semilinear parabolic equation; Monostable equation; Nonlocal nonlinearity |
College: |
Faculty of Science and Engineering |
Issue: |
05 |
Start Page: |
1850037 |