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A General Approach for Front-Propagation in Functional Reaction-Diffusion Equations

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Abstract

We investigate the persistence of front propagation for functional reaction-diffusion equations

$$v_\tau = v_{xx} + F(v)$$

where F is a given operator. By combining the upper and lower solution method with fixed point techniques, we prove a general existence theorem for traveling waves. Our result applies to reaction-diffusion equation with delayed or non-local reaction term.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131, Ancona, Italy

    Alessandro Calamai, Cristina Marcelli & Francesca Papalini

Authors
  1. Alessandro Calamai
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  2. Cristina Marcelli
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  3. Francesca Papalini
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Correspondence to Francesca Papalini.

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Calamai, A., Marcelli, C. & Papalini, F. A General Approach for Front-Propagation in Functional Reaction-Diffusion Equations. J Dyn Diff Equat 21, 567–593 (2009). https://doi.org/10.1007/s10884-009-9153-6

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  • DOI: https://doi.org/10.1007/s10884-009-9153-6

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