DEVELOPMENT OF FUSHCHICH'S MATHEMATICAL MODEL OF HEAT TRANSFER

For the fourth-order partial diff erential equation proposed by Fushchich for mathematical description of heat and mass transfer processes, the class of uniqueness and the class of correctness of the Cauchy problem have been established. Using the Fourier transform, a solution to the Cauchy problem is found in an explicit analytical form. It is shown that the new equation does not improve the properties of the classical heat conduction equation, but it allows one to describe heat transfer processes taking into account relaxation eff ects within the framework of the Galileo-invariant mathematical theory of transfer.
For the fourth-order partial diff erential equation proposed by Fushchich for mathematical description of heat and mass transfer processes, the class of uniqueness and the class of correctness of the Cauchy problem have been established. Using the Fourier transform, a solution to the Cauchy problem is found in an explicit analytical form. It is shown that the new equation does not improve the properties of the classical heat conduction equation, but it allows one to describe heat transfer processes taking into account relaxation eff ects within the framework of the Galileo-invariant mathematical theory of transfer.
Author:  V. I. Korzyuk, Ya. V. Rud'ko
Keywords:  parabolic equation, Cauchy problem, uniqueness class, correctness class, biparabolic heat conduction equation, Fourier transform, Duhamel principle, heat fl ux
Page:  451