Inverse problem for a fourth-order parabolic equation considering the additional high-order derivative in the initial condition.
Inverse problem for a fourth-order parabolic equation considering the additional high-order derivative in the initial condition.
Abstract
Introduction
We consider an inverse problem in this article. Actually, when high-order derivatives with respect
to t, exceeding the order of the equation are specified in the initial conditions.
A.N. Tikhonov was the first to study the problem with a high-order derivative on part of the domain
boundary. A problem for the homogeneous heat equation with the following conditions was studied in [1]
References
Tikhonov A.N. On boundary conditions containing derivatives of order exceeding the order of the equation. Math. collection. 1950. V. 26, issue 1. P. 35-56.
Bitsadze A.V. To the Neumann problem for harmonic functions. Reports of the Academy of Sciences of the USSR. 1990. V. 311, p. 11-13.
Moiseev E.I. On the solution of a nonlocal boundary value problem by the spectral method. Differentialequations. 1999, V. 35, No.8, p. 1094-1100.
