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March/April 2013 Optimal control problems of phase field system with total variation functional as the interfacial energy
Ken Shirakawa, Noriaki Yamazaki
Adv. Differential Equations 18(3/4): 309-350 (March/April 2013).

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.

Citation

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Ken Shirakawa. Noriaki Yamazaki. "Optimal control problems of phase field system with total variation functional as the interfacial energy." Adv. Differential Equations 18 (3/4) 309 - 350, March/April 2013.

Information

Published: March/April 2013
First available in Project Euclid: 5 February 2013

zbMATH: 1302.49007
MathSciNet: MR3060198

Subjects:
Primary: 35K55 , 35R35 , 49J20

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 3/4 • March/April 2013
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