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arXiv · 1702.08076

The hair-trigger effect for a class of nonlocal nonlinear equations

Dmitri Finkelshtein·Pasha Tkachov
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Abstract

We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on $\mathbb{R}^d$ 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 $\mathbb{R}^d$. We find also sufficient conditions for existence, uniqueness and comparison principle in the considered equations.

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Dmitri Finkelshtein, Pasha Tkachov. 2017-02-26. The hair-trigger effect for a class of nonlocal nonlinear equations. https://doi.org/10.1088/1361-6544/aab1cb

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