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Optimal control of nonlinear evolution equations associated with time-dependent subdifferentials and applications

Noriaki Yamazaki — 2009

Banach Center Publications

In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results.

A phase-field model of grain boundary motion

Akio ItoNobuyuki KenmochiNoriaki Yamazaki — 2008

Applications of Mathematics

We consider a phase-field model of grain structure evolution, which appears in materials sciences. In this paper we study the grain boundary motion model of Kobayashi-Warren-Carter type, which contains a singular diffusivity. The main objective of this paper is to show the existence of solutions in a generalized sense. Moreover, we show the uniqueness of solutions for the model in one-dimensional space.

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