New effects in propagation of waves for reaction–diffusion systems

Article type: Research Article

Authors: Vakulenko, S. | Volpert, V.

Affiliations: Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, 199178 Saint Petersburg, Russia E‐mail: vakul@microm.ipme.ru | Analyse numérique, Université Lyon 1, UMR 5585 CNRS, 69622 Villeurbanne, France E‐mail: volpert@lan.univ‐lyon1.fr

Abstract: The Cauchy problem for reaction–diffusion systems is studied. A notion of generalized travelling waves (GTW) is introduced to describe the large time behavior of solutions, in particular for the case of a nonhomogeneous medium. If the nonhomogeneous perturbation is asymptotically small, existence and stability of GTW is proved and their velocity is found. If the unperturbed systems is decoupled, the behavior of GTW for the perturbed system can be periodic or even chaotic both for homogeneous and nonhomogeneous perturbations. Dispersion of GTW on nonhomogeneities and applications to combustion problems are discussed.

Keywords: travelling waves, reaction–diffusion systems, attractors

Journal: Asymptotic Analysis, vol. 38, no. 1, pp. 11-33, 2004