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Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions

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Abstract

The paper deals with semilinear evolution equations in Banach spaces. By means of linear control terms, the controllability problem is investigated and the solutions satisfy suitable nonlocal conditions. The Cauchy multi-point condition and the mean value condition are included in the present discussion. The final configuration is always achieved with a control with minimum norm. The results make use of fixed point techniques; two different approaches are proposed, depending on the use of norm or weak topology in the state space. The discussion is completed with some applications to dynamics of diffusion processes.

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Acknowledgements

Funding was provided by Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni.

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Authors and Affiliations

  1. Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via Amendola, 2, 42122, Reggio Emilia, Italy

    Luisa Malaguti & Valentina Taddei

  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100, Toruń, Poland

    Krzysztof Rykaczewski

Authors
  1. Luisa Malaguti
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  2. Krzysztof Rykaczewski
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  3. Valentina Taddei
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Correspondence to Valentina Taddei.

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Malaguti, L., Rykaczewski, K. & Taddei, V. Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions. Mediterr. J. Math. 16, 78 (2019). https://doi.org/10.1007/s00009-019-1351-9

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  • DOI: https://doi.org/10.1007/s00009-019-1351-9

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