Abstract

In this paper, we analyze optimal control problems of semilinear parabolic equations, where the controls are distributed and depend only on time. Box constraints for the controls are imposed and the cost functional does not involve the control itself, only the associated state. We prove second order optimality conditions for local strong minimizers, which are used to derive error estimates in the numerical approximation. First we estimate the difference between the discrete and continuous optimal states. In the last part, under an additional assumption on the optimal adjoint state, we prove error estimates for the controls and improve the estimates for the states.

Keywords

  1. optimal control
  2. bang-bang control
  3. semilinear parabolic equation
  4. optimality conditions
  5. error estimates

MSC codes

  1. 35K58
  2. 49K20
  3. 49M25

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 2515 - 2540
ISSN (online): 1095-7138

History

Submitted: 21 February 2018
Accepted: 30 May 2019
Published online: 23 July 2019

Keywords

  1. optimal control
  2. bang-bang control
  3. semilinear parabolic equation
  4. optimality conditions
  5. error estimates

MSC codes

  1. 35K58
  2. 49K20
  3. 49M25

Authors

Affiliations

Funding Information

Ministerio de Economía, Industria y Competitividad, Gobierno de España https://doi.org/10.13039/501100010198 : MTM2014-57531-P, MTM2017-83185-P

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