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Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations

Dmitri Finkelshtein Orcid Logo, Yuri Kondratiev, Pasha Tkachov Orcid Logo

Electronic Journal of Differential Equations, Volume: 2019, Issue: 10, Pages: 1 - 27

Swansea University Author: Dmitri Finkelshtein Orcid Logo

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Abstract

We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on R^d. Using the properties of the corresponding semiflow, we prove the existence of monotone traveling waves along...

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Published in: Electronic Journal of Differential Equations
ISSN: 1072-6691
Published: 601 University Drive, San Marcos, TX 78666, USA Department of Mathematics, Texas State University 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa48385
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Abstract: We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on R^d. Using the properties of the corresponding semiflow, we prove the existence of monotone traveling waves along those directions where the diffusion kernel is exponentially integrable. Among other properties, we prove continuity, strict monotonicity and exponential integrability of the traveling wave profiles.
Keywords: Nonlocal diffusion; reaction-diffusion equation; Fisher-KPP equation; traveling waves; nonlocal nonlinearity; anisotropic kernels; integral equation.
College: Faculty of Science and Engineering
Issue: 10
Start Page: 1
End Page: 27

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