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Uniqueness of travelling waves for nonlocal monostable equations. (English) Zbl 1061.45003
The authors study uniqueness of travelling waves of two nonlocal models. One is the integro-differential equation $$u_t= J* u- u+ f(u),\tag1$$ where $J* u(z)= \int_{\bbfR^1} J(z-y) u(y)\,dy$, with $J\ge 0$, even, compactly supported and $\int_{\bbfR^1} J=1$. The second model is a discrete version of (1), namely, an infinite ordinary differential equation system $$\dot u_n= (J* u)_n- u_n+ f(u_n),\quad n\in\bbfZ,$$ where $(J* u)_n= \sum_{|i|\ge 1} J(n- i)u_i$ and $J$ and $f$ as in (1). To this end the authors use a Tauberian theorem for the Laplace transform.

45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations
34A34Nonlinear ODE and systems, general
45M05Asymptotic theory of integral equations
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