An optimal control problem for the Oskolkov equation
type: Item
instance of: scholarly article
title: An optimal control problem for the Oskolkov equation
zbMATH Open document ID: 1029.35077
DOI: 10.1023/A:1021136520119
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: In this short communication the authors consider the Cauchy-Dirichlet problem for the equation \[ (1- \kappa\Delta) \Delta\partial\psi/\partial t= \nu\Delta^2\psi- \partial(\psi, \Delta\psi)/\partial(x, y)+ u \] on the cylinder \(\Omega\times \mathbb{R}\), where \(\Omega\) is a bounded domain in \(\mathbb{R}^2\) with \(C^\infty\) boundary \(\partial\Omega\). The problem, which models the dynamics of certain viscoelastic incompressible fluids, is transformed into the Cauchy problem for a semilinear operator equation. The authors present conditions ensuring that the latter problem admits a unique solution \(v\in H^1((0,\tau);{\mathcal V})\), where \[ {\mathcal V}= \{v\in W^4_2(\Omega): v(x)=\Delta v(x)= 0, x\in\partial\Omega\}. \] An associated optimal control problem with respect to \(u\) is also considered.
reviewed by: Winfried Schirotzek
Mathematics Subject Classification ID: 35G25
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 58E25
Mathematics Subject Classification ID: 35B37
zbMATH DE Number: 1916141
zbMATH Keywords: Cauchy-Dirichlet problem
zbMATH Keywords: Cauchy problem
zbMATH Keywords: optimal control
author: Georgiĭ Anatol'evich Sviridyuk
author: Marina Vasilyevna Plekhanova
MaRDI profile type: Publication
full work available at URL: a:1021136520119
OpenAlex ID: W34303299
description: scientific article; zbMATH DE number 1916141