Mathematics

The inverse problem of recovering a leading coefficient in the two-dimensional heat equation

B. N. Tsybikov

Ugra State University, 16 Chehova St., Khanty-Mansyisk 628012, Russia

Abstract: We consider the inverse problem of recovering a leading coefficient independent of one of the spatial variable $y$ in the two-dimensional heat equation. The overdetermination data is the values of the solution on the cross-section of the domain by the hyperplane $y=0$. The solution is sought in the class of functions whose Fourier image in the variable $y$ is compactly supported in the dual variable. Existence and uniqueness conditions of the solution to this problem in this class are established.

Keywords: inverse problem, overdetermination condition, second order parabolic equation, initial-boundary value problem.

UDC: 517.95

Received: 28.01.2017

Bibliographic databases:

•