# Ivanchov N. I.

### Inverse problem for the heat equation in a rectangular domain

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 12. - pp. 1605-1614

We establish conditions for the existence and uniqueness of a smooth solution to the inverse problem for the two-dimensional heat equation with unknown leading coefficient depending on time and the space variable.

### Inverse Problem for a Two-Dimensional Diffusion Equation in a Domain with Free Boundary

Ivanchov N. I., Pabyrivs’ka N. V.

Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 917–927

We establish conditions for the existence and uniqueness of a smooth solution to the inverse problem for a two-dimensional diffusion equation with unknown time-dependent leading coefficient in a domain with free-boundary. The equation of unknown boundary is given in the form of the product of a known function of space variables and an unknown time-dependent function.

### Inverse problem for the strongly degenerate heat equation in a domain with free boundary

Hryntsiv N. M., Ivanchov N. I.

Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 28-43

In a domain with free boundary, we establish conditions for the existence and uniqueness of a solution of the inverse problem of finding the time-dependent coefficient of heat conductivity. We study the case of strong degeneration where the unknown coefficient tends to zero as $t → +0$ as a power function $t^{β}$, where $β ≥ 1$.

### Inverse problem for a parabolic equation with strong power degeneration

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1487–1500

We consider the inverse problem of determining the time-dependent coefficient of the leading derivative in a full parabolic equation under the assumption that this coefficient is equal to zero at the initial moment of time. We establish conditions for the existence and uniqueness of a classical solution of the problem under consideration.

### Inverse problem for the heat equation with degeneration

Ukr. Mat. Zh. - 2005. - 57, № 11. - pp. 1563–1570

We consider the inverse problem of determining the time-dependent thermal diffusivity that is equal to zero at the initial moment of time. We establish conditions for the existence and uniqueness of a classical solution of the problem under consideration.

### Inverse Problem with Free Boundary for Heat Equation

Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 901-910

We establish conditions for the existence and uniqueness of a solution of the inverse problem for a one-dimensional heat equation with unknown time-dependent leading coefficient in the case where a part of the boundary of the domain is unknown.

### Inverse problem of simultaneous determination of two coefficients in a parabolic equation

Ukr. Mat. Zh. - 2000. - 52, № 3. - pp. 329-335

We establish conditions for the unique existence of a solution of the inverse problem of simultaneous determination of two unknown coefficients in a parabolic equation. One of these coefficients is the leading coefficient that depends on time, and the other coefficient depends on a space variable.

### Inverse problems for the heat-conduction equation with nonlocal boundary conditions

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1066–1071

Conditions under which the time-dependent temperature conductivity coefficient is determined uniquely are established in the case where the boundary conditions and the overdetermination conditions are non local.