Mathematics

Decomposition of traveling waves problems

V. A. Sobolev^a, E. A. Tropkina^a, E. A. Shchepakina^a, L. Zhang<sup>b

a</sup> Samara National Research University, Samara, Russian Federation
^b Shandong University of Science and Technology, Qingdao, Shandong, China

Abstract: In the article, the traveling waves problem for singularly perturbed systems of semilinear parabolic equations is considered. An effective method for the order reduction of singularly perturbed systems is proposed. The obtained mathematical results are used to study traveling waves both for abstract partial differential equations and for a specific model that can arise in physics problems, chemistry, and biology.

Keywords: singular perturbations, slow invariant manifolds, critical travelling waves, singular, perturbations, integral manifold, order reduction, asymptotic expansion, differential equations, fast variables, slow variables.

UDC: 517.928

Received: 02.09.2021
Revised: 09.10.2021
Accepted: 15.11.2021

DOI: 10.18287/2541-7525-2021-27-3-22-30