Temporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observation

Qin Zhou; Binjie Li

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arXiv · 2006.04442

Temporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observation

Qin Zhou·Binjie Li

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Abstract

Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The convergence of a temporally semidiscrete approximation is rigorously established, where the control is not explicitly discretized and the state equation is discretized by a discontinuous Galerkin method in time. Numerical results are provided to verify the theoretical results.

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Qin Zhou, Binjie Li. 2020-06-08. Temporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observation. https://arxiv.org/abs/2006.04442

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