On the Existence of Optimal Control in the Problem of Optimizing the Lowest Coefficient of a Semilinear Evolutionary Equation

The paper studies the problem of optimizing the lowest coefficient understood as a function with values in a Banach space, which enters linearly into an abstract semilinear pseudoparabolic evolutionary differential equation in a Banach space. For this problem, an existence theorem for an optimal con...

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Vydáno v:Computational mathematics and mathematical physics Ročník 63; číslo 7; s. 1176 - 1190
Hlavní autor: Chernov, A. V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.07.2023
Springer Nature B.V
Témata:
Banach spaces
Computational Mathematics and Numerical Analysis
Differential equations
Existence theorems
Inverse problems
Mathematics
Mathematics and Statistics
Optimal Control
Optimization
Partial differential equations
semilinear evolution equation in a Banach space
Oskolkov’s system of equations
existence of an optimal control
ISSN:0965-5425, 1555-6662
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Shrnutí:The paper studies the problem of optimizing the lowest coefficient understood as a function with values in a Banach space, which enters linearly into an abstract semilinear pseudoparabolic evolutionary differential equation in a Banach space. For this problem, an existence theorem for an optimal control is proved. Due to the nonlinearity of the equation under study, the author uses his previous results on the total preservation of the unique global solvability (on the totally global solvability) and on the estimation of solutions for similar equations. This estimate turns out to be significant in the course of the study. As an example, the Oskolkov’s hydrodynamic system of equations is considered.
Bibliografie:ObjectType-Article-1
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523070035