Open AccessThe heat conduction model involving two temperatures on the segment with Wentzell boundary conditions
Author(s) -
N.S. Goncharov,
G. A. Sviridyuk
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1352/1/012022
Subject(s) - thermal conduction , mathematical analysis , heat kernel , bounded function , heat flux , isotropy , boundary value problem , boundary (topology) , laplace operator , heat equation , physics , space (punctuation) , relativistic heat conduction , mathematics , thermodynamics , heat transfer , quantum mechanics , linguistics , philosophy
According to the theory of relatively p -bounded operators, we study the Heat Conduction model involving two temperatures for isotropic material, which describes, the rate of change of internal energy due to the movement of the heat flux form one medium to its complement with general Wentzell boundary conditions. In particular, we consider spectrum of one-dimensional Laplace operator on the segment [0,1] with general Wentzell boundary conditions. We examine the relative spectrum in one-dimensional Heat Conduction equation involving two temperatures, and construct the resolving group in the Cauchy-Wentzell problem with general Wentzell boundary conditions. In the paper, these problems are solved under the assumption that the initial space is a contraction of the space L 2 (0,1).