论文标题
对单数抛物线PDE的最佳控制模型多相Stefan型自由边界问题
Optimal Control of Singular Parabolic PDEs Modeling Multiphase Stefan-type Free Boundary Problems
论文作者
论文摘要
分析了对多维和多相Stefan型自由边界问题的分布公式的最佳控制。有限维最佳控制问题的近似序列是通过有限差异引入的。在功能和控制方面都存在最佳控制和离散最佳控制问题序列的收敛性。特别是，在最小的规律性假设对系数上的最小规律性假设下，建立了有限差异方法的收敛以及存在，独特性和稳定性估计。
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.
