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.
Optimal controls for nonlocal Cauchy problems of multi-term fractional evolution equations
This paper is mainly concerned with a controlled multi-term fractional evolution equation in Banach spaces. Firstly, we give formula of its mild solutions and show the existence result for the problem via $\omega $-sectorial operator technique. Secondly, we establish the Lagrange optimal control and time optimal control for the system invoked by the nonlocal Cauchy problems of multi-term fractional evolution equation by properties of resolvent operators.
more » « less- PAR ID:
- 10372226
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- IMA Journal of Mathematical Control and Information
- Volume:
- 39
- Issue:
- 3
- ISSN:
- 0265-0754
- Page Range / eLocation ID:
- p. 912-929
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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