scholarly journals Inverse problem for semilinear ultraparabolic equation of higher order

2015 ◽  
Vol 140 (4) ◽  
pp. 395-404 ◽  
Author(s):  
Nataliya Protsakh
Keyword(s):  
Inverse Problem ◽  
Higher Order ◽  
Ultraparabolic Equation

scholarly journals Determining of right-hand side of higher order ultraparabolic equation

2017 ◽  
Vol 15 (1) ◽  
pp. 1048-1062 ◽  
Author(s):  
Nataliya Protsakh
Keyword(s):  
Inverse Problem ◽  
Existence And Uniqueness ◽  
Higher Order ◽  
Integral Type ◽  
Ultraparabolic Equation ◽  
Right Hand ◽  
Uniqueness Of The Solution ◽  
Time Variables

Abstract In the paper the conditions of the existence and uniqueness of the solution for the inverse problem for higher order ultraparabolic equation are obtained. The equation contains two unknown functions of spatial and time variables in its right-hand side. The overdetermination conditions of the integral type are used.

An inverse problem for a higher-order parabolic equation

1998 ◽  
Vol 64 (5) ◽  
pp. 590-599 ◽  
Author(s):  
V. L. Kamynin ◽  
E. Franchini
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Higher Order ◽  
Order Parabolic 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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