# Equations de reaction diffusion non-locale

Abstract : This PHD Thesis is devoted to the study of the exitence, uniqueness and qualitative behavior of travelling wave solutions of non-local reaction diffusion equations $u_(t)-(\int_(\R)J(x-y)[u(y)-u(x)]dy)=f(u)$. Such nonlinear equations arise in population dynamics or in neural network when considering non-local diffusion. We treat three different classes of nonlinearities $f$ (bistable, ignition, monostable), which are commonly used in the litterature. Existence for bistable and ignition nonlinearity are obtained using a homotopy argument. For monostable nonlinearity, existence is obtained through approximation problem set on semi infinite interval $(-r,+\infty)$. Uniqueness and monotonicity of the travelling wave are obtained using sliding techniques. Asympotic behavior and speed formula are also investigate.
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Cited literature [51 references]

https://tel.archives-ouvertes.fr/tel-00004313
Contributor : Jerome Coville <>
Submitted on : Monday, January 26, 2004 - 3:24:37 PM
Last modification on : Wednesday, December 9, 2020 - 3:09:36 PM
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• HAL Id : tel-00004313, version 1

### Citation

Jerome Coville. Equations de reaction diffusion non-locale. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2003. Français. ⟨tel-00004313⟩

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