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A Product Formula Approach to a Nonhomogeneous Boundary Optimal Control Problem Governed by Nonlinear Phase-field Transition System

Part I: A Phase-field Model

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Abstract

The paper establishes existence, uniqueness and regularity for the solution of a phase-field transition system with non-homogeneous Cauchy-Neumann boundary conditions. Moreover, some estimates for the solution are given. The non-linear parabolic problem considered here can be used to modeling the solidification (liquidification) process to a matter. The non-homogeneous boundary conditions (depending both on time and space variables) can be understood as a boundary control.

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Author information

Authors and Affiliations

  1. University of Bologna, 40126, Bologna, Italy

    Tommaso Benincasa & Angelo Favini

  2. University of Iaşi, 700506, Iasi, Romania

    Costică Moroşanu

Authors
  1. Tommaso Benincasa
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  2. Angelo Favini
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  3. Costică Moroşanu
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Corresponding author

Correspondence to Angelo Favini.

Additional information

Communicated by F. Giannessi.

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Benincasa, T., Favini, A. & Moroşanu, C. A Product Formula Approach to a Nonhomogeneous Boundary Optimal Control Problem Governed by Nonlinear Phase-field Transition System. J Optim Theory Appl 148, 14–30 (2011). https://doi.org/10.1007/s10957-010-9742-x

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  • DOI: https://doi.org/10.1007/s10957-010-9742-x

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