Advances in Differential Equations

Optimal control problems of phase field system with total variation functional as the interfacial energy

Ken Shirakawa and Noriaki Yamazaki

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we consider optimal control problems for one-dimensional phase field system with total variation functional as the interfacial energy. Our system consists of two parabolic PDEs: a heat equation and a singular diffusion equation of an order parameter. We prove the existence of an optimal control that minimizes the nonlinear and nonsmooth cost functional. Moreover, we show the necessary condition of the optimal pair by using the optimal control problem of the approximating system.

Article information

Source
Adv. Differential Equations Volume 18, Number 3/4 (2013), 309-350.

Dates
First available in Project Euclid: 5 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1360073019

Mathematical Reviews number (MathSciNet)
MR3060198

Zentralblatt MATH identifier
1302.49007

Subjects
Primary: 49J20: Optimal control problems involving partial differential equations 35K55: Nonlinear parabolic equations 35R35: Free boundary problems

Citation

Shirakawa, Ken; Yamazaki, Noriaki. Optimal control problems of phase field system with total variation functional as the interfacial energy. Adv. Differential Equations 18 (2013), no. 3/4, 309--350. https://projecteuclid.org/euclid.ade/1360073019.


Export citation