Dmitri Finkelshtein, Yuri Kondratiev, Pasha Tkachov
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.
Submitted July 2, 2018. Published Janaury 22, 2019.
Math Subject Classifications: 35C07, 35K57, 45G10.
Key Words: Nonlocal diffusion; reaction-diffusion equation; Fisher-KPP equation;
traveling waves; nonlocal nonlinearity; anisotropic kernels;
integral equation.
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Dmitri Finkelshtein Department of Mathematics Swansea University, Bay Campus Fabian Way, Swansea SA1 8EN, UK email: d.l.finkelshtein@swansea.ac.uk |
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Yuri Kondratiev Fakultät für Mathematik Universität Bielefeld, Postfach 110 131 33501 Bielefeld, Germany email: kondrat@math.uni-bielefeld.de |
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Pasha Tkachov Gran Sasso Science Institute Viale Francesco Crispi, 7 67100 L'Aquila AQ, Italy email: pasha.tkachov@gssi.it |
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