This article is cited in 2 papers

Differentical equations, dynamical systems and optimal control

Justification of asymptotic decomposition of a solution for the problem of the motion of weak solutions of polymers near a critical point

A. G. Petrova

Altai State Unuversity, 61, Lenina ave., Barnaul, 630090, Russia

Abstract: We consider the boundary-value problem in a semibounded interval for a third-order integro-differential equation with the small parameter multiplies the product of the integral of unknown function vanishing on the boundary and its highest derivative. Such a problem arises in the description of the motion of weak solutions of polymers near a critical point. Unique solvability for the problem for all values of the parameter in [0,1] is proved in [1]. In this paper the representation of a solution as an asymptotic series in non-negative integer powers of the small parameter is established.

Keywords: flow of an aqueous solution of polymers, boundary-value problem in a semibounded interval, small parameter, asymptotic solution.

UDC: 517.928

MSC: 34E05, 34K10

Received December 9, 2019, published March 4, 2020

DOI: 10.33048/semi.2020.17.020

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