# Frechet differentiability in Besov spaces in the optimal control of parabolic free boundary problems

@article{Abdulla2016FrechetDI, title={Frechet differentiability in Besov spaces in the optimal control of parabolic free boundary problems}, author={Ugur G. Abdulla and Jonathan Goldfarb}, journal={Journal of Inverse and Ill-posed Problems}, year={2016}, volume={26}, pages={211 - 227} }

Abstract We consider the inverse Stefan type free boundary problem, where information on the boundary heat flux and the density of the sources are missing and must be found along with the temperature and the free boundary. We pursue the optimal control framework analyzed in [1, 2], where the boundary heat flux, the density of the sources, and the free boundary are components of the control vector. We prove the Frechet differentiability in Besov spaces, and derive the formula for the Frechet…

#### 11 Citations

On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems

- Mathematics
- 2017

We consider the inverse Stefan type free boundary problem, where the coefficients, boundary heat flux, and density of the sources are missing and must be found along with the temperature and the free…

N ov 2 01 7 ON THE STATE CONSTRAINED OPTIMAL CONTROL OF THE STEFAN TYPE FREE BOUNDARY PROBLEMS

- 2018

We analyze the state constrained inverse Stefan type parabolic free boundary problem as an optimal control problem in the Sobolev-Besov spaces framework. Boundary heat flux, density of heat sources,…

Gradient method in Hilbert-Besov spaces for the optimal control of parabolic free boundary problems

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Computational analysis of the inverse Stefan type free boundary problem, where information on the boundary heat flux is missing and must be found along with the temperature and the free boundary, and optimal control framework introduced in Abdulla is pursued.

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The Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity tensor and potential in the body based on the measurement of the boundary voltages on the electrodes…

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