For further information or to suggest a speaker for the PDE Seminear contact:
Misha Perepelitsa (maperepelitsa AT uh DOT edu)
Gabriela Jaramillo (gtjaramillo AT uh DOT edu)
William Fitzgibbon (fitz AT uh DOT edu)
Fall 2024
Fridays 2-3pm (CST) in PGH 646
November 1
Speaker: Joshua Siktar (TAMU)
Title: Existence of Solutions for Fractional Optimal Control Problems with Minimax Constraint
Abstract:
In this talk we prove the existence of solutions to an optimal control problem where the constraint is an ill-posed, nonlinear equation containing a Fractional Laplacian. For any fixed control data, the constraint equation is known to have multiple solutions by a previous application of the Mountain Pass Theorem. Due to the pointwise nature of the conditions on controls needed to invoke this theorem, we must make substantial adaptations to the usual direct method of calculus of variations in order to prove our main existence result. The main theoretical tools are a thoughtful construction of an admissible set of controls, and a technical lemma that ensures that a minimizing sequence of pairs of controls and corresponding states exhibits convergence to another control-state pair that satisfies the constraint equation.
November 22
Speaker: Jimmie Adriazola (SMU)
Title: TBD
Abstract: TBD