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A contact problem of a thermoelastic diffusion rod
Author(s) -
Aouadi M.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900312
Subject(s) - thermoelastic damping , sobolev space , mathematics , mathematical analysis , nonlinear system , infinity , heat equation , diffusion , boundary (topology) , space (punctuation) , zero (linguistics) , physics , thermal , thermodynamics , computer science , linguistics , philosophy , quantum mechanics , operating system
We consider a one‐dimensional contact problem in linear thermoelastic diffusion theory. The coupled system of equations consists of a hyperbolic equation and two parabolic equations. This problem poses new mathematical difficulties due to the nonlinear boundary conditions. The existence of a weak solution is proved by the use of Sobolev's basic space energy arguments. Moreover, we show that the weak solution converges to zero exponentially as time goes to infinity.