Abstract
In this chapter we consider several reaction-diffusion systems—known as road-field systems—which describe the effect that one (or two) line(s) with heterogeneous diffusion has (have) on the speed of propagation in a planar domain, where the classical Fisher-KPP equation is considered. We recall the results by Berestycki et al. (J. Math. Biol. 66:743–766, 2013) for the case of a line in a half-plane, and those obtained in collaboration with Rossi et al. (SIAM J. Math. Anal. 49, 4595–4624, 2017) for two lines bounding a strip. The main goal is to compare the speed of propagation in the direction of the line(s) of these situations with the cases of a plane with one and two lines on which the diffusion is different with respect to the rest of the planar domain.
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Notes
- 1.
This symmetry condition is not required—and even meaningless—when the domain is the upper half-plane.
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Acknowledgements
This work has been supported by the Spanish Ministry of Economy, Industry and Competitiveness through contract Juan de la Cierva Incorporación IJCI-2015-25084 and project MTM2015-65899-P, and by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n.321186—ReaDi “Reaction-Diffusion Equations, Propagation and Modelling”.
The author wishes to thank the anonymous referee for his/her comments which have improved the presentation of the results of this work.
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Tellini, A. (2019). Comparison Among Several Planar Fisher-KPP Road-Field Systems. In: Dipierro, S. (eds) Contemporary Research in Elliptic PDEs and Related Topics. Springer INdAM Series, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-18921-1_12
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