On an optimal control problem of time-fractional advection-diffusion equation

Qing Tang

doi:10.3934/dcdsb.2019266

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2020, Volume 25, Issue 2: 761-779. Doi: 10.3934/dcdsb.2019266

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On an optimal control problem of time-fractional advection-diffusion equation

Qing Tang^,

China university of Geosciences, Wuhan, Hubei province, China

^* Corresponding author: Qing Tang
^* Corresponding author: Qing Tang

Received: December 31, 2018

Revised: March 31, 2019

Early access: November 2019

Published: February 2020

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Abstract

We consider an optimal control problem of an advection-diffusion equation with Caputo time-fractional derivative. By convex duality method we obtain as optimality condition a forward-backward coupled system. We then prove the existence of a solution to this coupled system using Schauder fixed point theorem. The uniqueness of the solution is also established under certain monotonicity condition on the cost functional.

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Mathematics Subject Classification: Primary: 35R11, 60H05, 26A33, 40L20.

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