SOLUTION OF NONSTATIONARY PROBLEMS OF HEAT CONDUCTION FOR 
CURVILINEAR REGIONS BY DIRECT CONSTRUCTION OF EIGENFUNCTIONS

A. D. Chernyshov

UDC 536

By separation of a time variable, the nonstationary problem 
is reduced to a problem on eigenvalues and eigenfunctions. The method 
of superposition of geometrically one-dimensional F
(I solutions, where (I are special variables, 
is employed to solve it. The integral superposition of the functions 
F(I yields the solution assumed. Fulfillment 
of the boundary conditions leads to the problem on eigenfunctions 
in the form of a generalized Fredholm integral equation of the first 
kind with known simple kernels. The resulting approximate solution 
of the nonstationary problem has the analytical form of a finite sum; 
it exactly satisfies the initial differential equation, the initial 
conditions, and the boundary conditions at the points of division 
of the boundary into small portions and approximately satisfies just 
the conditions between these points. A theorem on the possibility 
of multiplying together eigenfunctions which can be employed for regions 
of complex shape has been proved.

Voronezh State Technological Academy, 19 Revolyutsiya 
Ave., Voronezh, 394000, Russia. Translated from Inzhenerno-Fizicheskii 
Zhurnal, Vol. 77, No. 2, pp. 160-166, March-April, 2004. Original 
article submitted July 23, 2002; revision submitted July 29, 2003.