Traveling waves for a reaction–diffusion–advection system with interior or boundary losses

Thomas Giletti

doi:10.1016/j.crma.2011.04.002

Partial Differential Equations

Traveling waves for a reaction–diffusion–advection system with interior or boundary losses
[Étude dʼun système de réaction–diffusion avec pertes]

Présenté par : Haïm Brezis

Thomas Giletti ¹

¹ Université Aix-Marseille III, LATP, faculté des sciences et techniques, avenue Escadrille Normandie–Niemen, 13397 Marseille cedex 20, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 535-539.

Abstract (VO)
Résumé

This Note deals with the existence and qualitative properties of traveling wave solutions of a nonlinear reaction–diffusion system with losses inside the domain. In particular, we show the existence of a continuum of admissible speeds of traveling waves. Lastly, by considering losses concentrated near the boundary of the domain, these results are compared with those already known in the case of losses on the boundary.

Cette Note a pour objet lʼexistence et les propriétés des solutions de type front progressif pour un système de réaction–diffusion non linéaire avec pertes à lʼintérieur du domaine. Nous montrons en particulier lʼexistence dʼun continuum de vitesses admissibles pour les fronts. Enfin, en considérant des pertes localisées près du bord, ces résultats sont comparés avec ceux déjà connus pour des pertes à la frontière du domaine.

Reçu le : 2010-08-11
Accepté le : 2011-04-11
Publié le : 2011-05-01

DOI : 10.1016/j.crma.2011.04.002

Affiliations des auteurs :

Thomas Giletti ¹

¹ Université Aix-Marseille III, LATP, faculté des sciences et techniques, avenue Escadrille Normandie–Niemen, 13397 Marseille cedex 20, France

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     author = {Thomas Giletti},
     title = {Traveling waves for a reaction{\textendash}diffusion{\textendash}advection system with interior or boundary losses},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {535--539},
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     doi = {10.1016/j.crma.2011.04.002},
     language = {en},
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Thomas Giletti. Traveling waves for a reaction–diffusion–advection system with interior or boundary losses. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 535-539. doi : 10.1016/j.crma.2011.04.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.04.002/

Bibliographie
Cité par

[1] H. Berestycki, F. Hamel, Reaction–Diffusion Equations and Propagation Phenomena, Springer-Verlag, in press.

[2] H. Berestycki; F. Hamel; A. Kiselev; L. Ryzhik Quenching and propagation in KPP reaction–diffusion equations with a heat loss, Arch. Ration. Mech. Anal., Volume 178 (2005), pp. 57-80

[3] H. Berestycki; L. Nirenberg Traveling wave in cylinders, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 9 (1992), pp. 497-572

[4] T. Giletti KPP reaction–diffusion equations with a non-linear loss inside a cylinder, Nonlinearity, Volume 23 (2010), p. 2307

[5] T. Giletti, KPP reaction–diffusion system with loss inside a cylinder: convergence toward the problem with Robin boundary conditions, preprint.

[6] F. Hamel; L. Ryzhik Non-adiabatic KPP fronts with an arbitrary Lewis number, Nonlinearity, Volume 18 (2005), pp. 2881-2902

[7] J.D. Murray Mathematical Biology, Springer, 2003

[8] J. Xin Analysis and modelling of front propagation in heterogeneous media, SIAM Rev., Volume 42 (2000), pp. 161-230

Mostafa Zahri Numerical Treatment of Multidimensional Stochastic, Competitive and Evolutionary Models, Disease Prevention and Health Promotion in Developing Countries (2020), p. 183 | DOI:10.1007/978-3-030-34702-4_13
Mostafa Zahri, 2019 8th International Conference on Modeling Simulation and Applied Optimization (ICMSAO) (2019), p. 1 | DOI:10.1109/icmsao.2019.8880436
Mostafa Zahri Barycentric interpolation of interface solution for solving stochastic partial differential equations on non-overlapping subdomains with additive multi-noises, International Journal of Computer Mathematics, Volume 95 (2018) no. 4, pp. 645-685 | DOI:10.1080/00207160.2017.1297429 | Zbl:1390.35165

Cité par 3 documents. Sources : Crossref, zbMATH

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