New effects in propagation of waves for reaction–diffusion systems

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.