Journal article 977 views 173 downloads
The hair-trigger effect for a class of nonlocal nonlinear equations
Dmitri Finkelshtein 
,
Pasha Tkachov
,
Pasha Tkachov
Nonlinearity, Volume: 31, Issue: 6, Pages: 2442 - 2479
Swansea University Author:
Dmitri Finkelshtein
DOI (Published version): 10.1088/1361-6544/aab1cb
Abstract
We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and \theta>0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to \infty) to \t...
| Published in: | Nonlinearity |
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| ISSN: | 0951-7715 1361-6544 |
| Published: |
IOP Publishing
2018
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa38865 |
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| Abstract: |
We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on R^d which have only two constant stationary solutions, 0 and \theta>0. The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to \infty) to \theta locally uniformly in R^d. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations. |
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| Keywords: |
hair-trigger effect, nonlocal diffusion, reaction-diffusion equation, front propagation, monostable equation, nonlocal nonlinearity, long-time behavior, integral equation |
| College: |
Faculty of Science and Engineering |
| Issue: |
6 |
| Start Page: |
2442 |
| End Page: |
2479 |