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Title: 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.  more » « less
Award ID(s):
1818772
NSF-PAR ID:
10175696
Author(s) / Creator(s):
;
Date Published:
Journal Name:
ESAIM: Control, Optimisation and Calculus of Variations
Volume:
26
ISSN:
1292-8119
Page Range / eLocation ID:
5
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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