Free Boundary Problem in a Polymer Solution Model

A. G. Petrova, V. V. Pukhnachev

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)96-103
Number of pages8
JournalRussian Journal of Mathematical Physics
Volume28
Issue number1
DOIs
Publication statusPublished - Jan 2021

OECD FOS+WOS

  • 1.01 MATHEMATICS
  • 1.03 PHYSICAL SCIENCES AND ASTRONOMY

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