Traveling wave solutions for monotone systems of impulsive reaction-diffusion equations

Yatat Valaire, Banasiak Jacek, Dumont Yves. 2019. Traveling wave solutions for monotone systems of impulsive reaction-diffusion equations. In : Book of abstracts of the conference on mathematical methods and models in biosciences 16th-22nd of june 2019, Bedlewo, Poland. University of Warsaw, Banach Center, Institute of Mathematics of Polish Academy of Sciences, Biomath Forum, Mathematical Biosciences Institute, Ohio State University, Łódź University of Technology, University of Pretoria, Bulgarian Academy of Sciences. Bedlowo : University of Warsaw, Résumé, p. 86. Biomath 2019: international conference on Mathematical Methods and Models in Biosciences, Bedlowo, Pologne, 16 June 2019/22 June 2019.

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Abstract : Many systems in life sciences have been modeled by Reaction Diffusion Equations (RDE). However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release) such that an appropriate formalism is necessary, using, for instance, Impulsive Reaction Diffusion Equations (IRDE). While the study of traveling waves for monotone RDE has been done in several works, like [2], very little has been done in the case of (monotone) IRDE. Based on recursion equations theory [1], we aim to present in this talk a generic framework that handles two main issues of IRDE. First, it allows the characterization of spreading speeds in monotone systems of IRDE. Second, it deals with the existence of traveling waves for (nonlinear) monotone systems of IRDE. We apply our methodology to a system of IRDE that models tree-grass interactions in fire-prone savanna [4], extending the result obtained in [3].

Mots-clés libres : Impulsive differential equation, Impulsive event, Partial differential equations, Traveling wave solution, Qualitative analysis, Numerical simulations, Fire, Savanna dynamics, Forest dynamics

Auteurs et affiliations

  • Yatat Valaire, University of Pretoria (ZAF)
  • Banasiak Jacek, University of Pretoria (ZAF)
  • Dumont Yves, CIRAD-BIOS-UMR AMAP (ZAF) ORCID: 0000-0003-4817-685X

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