Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions

Luisa Malaguti; Krzysztof Rykaczewski; Valentina Taddei

doi:10.1007/s00009-019-1351-9

Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions

Luisa Malaguti, Krzysztof Rykaczewski, Valentina Taddei

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Article number	78
Journal	Mediterranean Journal of Mathematics
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/s00009-019-1351-9
State	Published - Jun 1 2019
Externally published	Yes

Funding

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

Funders	Funder number
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

Keywords

Controllability
fixed point
mild solution
nonlocal solution
semilinear differential inclusion

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10.1007/s00009-019-1351-9

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title = "Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions",

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.",

keywords = "Controllability, fixed point, mild solution, nonlocal solution, semilinear differential inclusion",

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AU - Malaguti, Luisa

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AU - Taddei, Valentina

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N2 - 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.

AB - 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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KW - semilinear differential inclusion

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ER -

Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions

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Keywords

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