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Optimal Control of Nonclassical Diffusion Equations with Memory

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Abstract

In this paper we consider an optimal control problem of nonclassical diffusion equations with memory. We investigate the existence and uniqueness of optimal solutions. The necessary and sufficient optimality conditions are also studied. The main novelty of our result is to establish the optimality conditions for the parabolic optimal control problem with memory.

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Acknowledgements

The author would like to thank the reviewers for the helpful comments and suggestions which improved the presentation of the paper. This work was completed while the author was visiting the Vietnam Institute of Advanced Study in Mathematics (VIASM). The author would like to thank the Institute for its hospitality.

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2018.303.

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  1. Department of Mathematics, Haiphong University, 171 Phan Dang Luu, Kien An, Haiphong, Vietnam

    Nguyen Duong Toan

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Toan, N.D. Optimal Control of Nonclassical Diffusion Equations with Memory. Acta Appl Math 169, 533–558 (2020). https://doi.org/10.1007/s10440-020-00310-4

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