We consider optimal control of fractional in time (subdiffusive, i.e., for
Optimal control of fractional semilinear PDEs
In this paper, we consider the optimal control of semilinear fractional PDEs with both spectral and integral fractional diffusion operators of order 2 s with s ∈ (0, 1). We first prove the boundedness of solutions to both semilinear fractional PDEs under minimal regularity assumptions on domain and data. We next introduce an optimal growth condition on the nonlinearity to show the Lipschitz continuity of the solution map for the semilinear elliptic equations with respect to the data. We further apply our ideas to show existence of solutions to optimal control problems with semilinear fractional equations as constraints. Under the standard assumptions on the nonlinearity (twice continuously differentiable) we derive the first and second order optimality conditions.
 Award ID(s):
 1818772
 Publication Date:
 NSFPAR ID:
 10175696
 Journal Name:
 ESAIM: Control, Optimisation and Calculus of Variations
 Volume:
 26
 Page Range or eLocationID:
 5
 ISSN:
 12928119
 Sponsoring Org:
 National Science Foundation
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