TY - JOUR

T1 - Free Boundary Problem in a Polymer Solution Model

AU - Petrova, A. G.

AU - Pukhnachev, V. V.

N1 - Funding Information: The research was financially supported by the Russian Foundation for Basic Research (project 19-01-0096). Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1

Y1 - 2021/1

N2 - An initial boundary value problem with a free boundary for a third-order integro-differential equation for the unsteady flow of an aqueous polymer solution in a strip is studied. Questions concerning the solvability of the problem and the qualitative behavior of the solution in dependence on the initial data are investigated: time-local resolvability is established under natural conditions on the input data and conditions of global solvability are found for the problem of strip narrowing. Conditions for the bowing-up of the solution in finite time in the model problem of strip expansion are presented. The problem of small perturbations of the flow of a strip of viscous fluid with respect to a parameter proportional to the relaxation viscosity is also consider.

AB - An initial boundary value problem with a free boundary for a third-order integro-differential equation for the unsteady flow of an aqueous polymer solution in a strip is studied. Questions concerning the solvability of the problem and the qualitative behavior of the solution in dependence on the initial data are investigated: time-local resolvability is established under natural conditions on the input data and conditions of global solvability are found for the problem of strip narrowing. Conditions for the bowing-up of the solution in finite time in the model problem of strip expansion are presented. The problem of small perturbations of the flow of a strip of viscous fluid with respect to a parameter proportional to the relaxation viscosity is also consider.

UR - http://www.scopus.com/inward/record.url?scp=85102742475&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/493b06d8-383c-3eaa-a8c2-18c7770486b4/

U2 - 10.1134/S1061920821010106

DO - 10.1134/S1061920821010106

M3 - Article

AN - SCOPUS:85102742475

VL - 28

SP - 96

EP - 103

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

SN - 1061-9208

IS - 1

ER -