Method of holomorphic regularization of the Cauchy problem for one class of nonlinear Tikhonov systems

D. A. Maslov

National Research University "Moscow Power Engineering Institute"

Abstract: In this paper, we consider the Cauchy problem for nonlinear Tikhonov systems, i.e., systems of differential equations some of which are singularly perturbed. We examine a special case where a part of the system with singularly perturbed equations is linear with respect to variables involving in the system with their derivatives. For the problem considered, we develop the holomorphic regularization method, namely, we introduce the concept of a pseudo-holomorphic solution, prove a theorem of the existence of such solution, and propose a procedure for calculating coefficients of series by degrees of the small parameter representing a pseudo-holomorphic solution.

Keywords: Tikhonov system of differential equations, small parameter, holomorphic regularization method

UDC: 517.928

MSC: 34E15

DOI: 10.36535/2782-4438-2025-244-79-85