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Paper detail

Optimal Control of Singular Parabolic PDEs Modeling Multiphase Stefan-type Free Boundary Problems

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control problems is introduced via finite differences. Existence of the optimal control and the convergence of the sequence of discrete optimal control problems both with respect to functional and control is proved. In particular, convergence of the method of finite differences, and existence, uniqueness and stability estimations are established for the singular PDE problem under minimal regularity assumptions on the coefficients.

preprint2020arXivOpen access
Ugur G. AbdullaEvan Cosgrove
math.APmath.OC
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Ugur G. AbdullaEvan Cosgrove

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