Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions
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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.
KeywordsControllability semilinear differential inclusion nonlocal solution mild solution fixed point
Mathematics Subject ClassificationPrimary 93B05 34A60 Secondary 34B15 47H04 47H09 47H10
Funding was provided by Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni.
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