Optimal Control of Solutions to Showalter–Sidorov Problem for a High Order Sobolev Type Equation with Additive “Noise”

2020 ◽  
pp. 435-446
Author(s):  
Alyona A. Zamyshlyaeva ◽  
Olga N. Tsyplenkova
Keyword(s):  
Optimal Control ◽  
Additive Noise ◽  
Type Equation ◽  
High Order ◽  
Sobolev Type ◽  
Sobolev Type Equation

scholarly journals Optimal control of solutions of a multipoint initial-final problem for non-autonomous evolutionary Sobolev type equation

2019 ◽  
Vol 8 (3) ◽  
pp. 473-488 ◽  
Author(s):  
Minzilia A. Sagadeeva ◽  
◽  
Sophiya A. Zagrebina ◽  
Natalia A. Manakova
Keyword(s):  
Optimal Control ◽  
Type Equation ◽  
Sobolev Type ◽  
Sobolev Type Equation

scholarly journals Optimal Control of Solutions to the Initial-Final Problem for the Sobolev Type Equation of Higher Order

2016 ◽  
Vol 3 (2) ◽  
pp. 57-67 ◽  
Author(s):  
A.A. Zamyshlyaeva ◽  
◽  
O.N. Tsyplenkova ◽  
E.V. Bychkov ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Type Equation ◽  
Higher Order ◽  
Sobolev Type ◽  
Sobolev Type Equation

On a nonlinear Sobolev type equation

2005 ◽  
Vol 41 (1) ◽  
pp. 146-149 ◽  
Author(s):  
I. A. Shishmarev
Keyword(s):  
Type Equation ◽  
Sobolev Type ◽  
Sobolev Type Equation

scholarly journals Inverse Problem for the Sobolev Type Equation of Higher Order

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1647
Author(s):  
Alyona Zamyshlyaeva ◽  
Aleksandr Lut
Keyword(s):  
Inverse Problem ◽  
Bounded Operator ◽  
Type Equation ◽  
Higher Order ◽  
Successive Approximations ◽  
Unknown Coefficient ◽  
Method Of Successive Approximations ◽  
Sobolev Type ◽  
Equivalent Problems ◽  
Sobolev Type Equation

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study.

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