Dept. Math, Hokkaido Univ. EPrints Server

OPTIMAL CONTROL OF A SINGULAR DIFFUSION EQUATION WITH CONSTRAINT

Preprint Series # 875
Ohtsuka, Takeshi and Shirakawa, Ken and Yamazaki, Noriaki OPTIMAL CONTROL OF A SINGULAR DIFFUSION EQUATION WITH CONSTRAINT. (2007);

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Abstract

In this paper, we consider an optimal control problem for a state problem of a one dimensional Allen-Cahn type equation, which is derived from a free energy including the total variation interfacial energy and the constraint by the indicator function. So, the state problem contains the singular diffusion coming from the total variation, and another singular term coming from the constraint. The main conclusions of this paper are concerned with the existence of an optimal control (optimal pair) and the necessary condition (optimality condition) of an optimal pair. Furthermore, the analytic methods, performed in this paper, will provide an effective approximating approach to the optimal pairs of our control problem.

Item Type:Preprint
Subjects:49-xx CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION
ID Code:1773