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Title: Optimal control of variably distributed‐order time‐fractional diffusion equation: Analysis and computation
Abstract

Fractional diffusion equations exhibit competitive capabilities in modeling many challenging phenomena such as the anomalously diffusive transport and memory effects. We prove the well‐posedness and regularity of an optimal control of a variably distributed‐order fractional diffusion equation with pointwise constraints, where the distributed‐order operator accounts for, for example, the effect of uncertainties. We accordingly develop and analyze a fully‐discretized finite element approximation to the optimal control without any artificial regularity assumption of the true solution. Numerical experiments are also performed to substantiate the theoretical findings.

 
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Award ID(s):
2245097 2012291
PAR ID:
10534013
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Wiley
Date Published:
Journal Name:
Numerical Methods for Partial Differential Equations
ISSN:
0749-159X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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