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1
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An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point

100%
Fedoseev A.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2203-2214
EN
We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.
2
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Determining of right-hand side of higher order ultraparabolic equation

100%
Protsakh N.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1048-1062
EN
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.
3
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Determination of a diffusion coefficient in a quasilinear parabolic equation

88%
Kanca F.
Open Mathematics
|
2017
|
tom 15
|
nr 1
77-91
EN
This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown. Finally, some numerical experiments are presented.
4
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Inverse problem for a physiologically structured population model with variable-effort harvesting

75%
Andrusyak R. V.
Open Mathematics
|
2017
|
tom 15
|
nr 1
433-445
EN
We consider the inverse problem of determining how the physiological structure of a harvested population evolves in time, and of finding the time-dependent effort to be expended in harvesting, so that the weighted integral of the density, which may be, for example, the total number of individuals or the total biomass, has prescribed dynamics. We give conditions for the existence of a unique, global, weak solution to the problem. Our investigation is carried out using the method of characteristics and a generalization of the Banach fixed-point theorem.
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