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September/October 2015 Traveling waves for a bistable equation with nonlocal diffusion
Franz Achleitner, Christian Kuehn
Adv. Differential Equations 20(9/10): 887-936 (September/October 2015).

Abstract

We consider a single component reaction-diffusion equation in one dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. Our main result shows the existence, uniqueness (up to translations) and local asymptotic stability of a traveling wave solution connecting two stable homogeneous steady states. In particular, we provide an extension to classical results on traveling wave solutions involving local diffusion. This extension to evolution equations with Riesz-Feller operators requires several technical steps. These steps are based upon an integral representation for Riesz-Feller operators, a comparison principle, regularity theory for space-fractional diffusion equations, and control of the far-field behavior.

Citation

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Franz Achleitner. Christian Kuehn. "Traveling waves for a bistable equation with nonlocal diffusion." Adv. Differential Equations 20 (9/10) 887 - 936, September/October 2015.

Information

Published: September/October 2015
First available in Project Euclid: 23 June 2015

zbMATH: 1327.35053
MathSciNet: MR3360395

Subjects:
Primary: 35A01, 35A09, 35R09, 47G20, 47G20

Rights: Copyright © 2015 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.20 • No. 9/10 • September/October 2015
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