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On the approximation method of solving integral equations in diffusion problems
Author(s) -
Bobula E.,
Twardowska K.,
Piskorek A.
Publication year - 1987
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670090117
Subject(s) - mathematics , contraction principle , integral equation , heat equation , mathematical analysis , domain (mathematical analysis) , contraction (grammar) , boundary value problem , convection–diffusion equation , heat flux , heat transfer , fixed point theorem , mechanics , physics , medicine
In this paper we consider the one‐dimensional problem of heat or mass transport in the system with moving ends. We show that without solving the heat transfer equation, the heat flux flowing out from the system can be found when temperature on the boundary of this system is known. We make use of the Banach contraction theorem for appropriate integral equations. Our method also enables us to find the distribution of temperature in the whole domain that forms the physical system.