Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Transmission Problem in Thermoelasticity | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 190548 33 pages doi 2011 190548 Research Article Transmission Problem in Thermoelasticity Margareth S. Alves 1 Jaime E. Munoz Rivera 2 Mauricio Sepulveda 3 and Octavio Vera Villagran4 1 Departamento de Matemdtica Universidade Federal de VÍỊosa UFV 36570-000 VÍỊosa MG Brazil 2 National Laboratory for Scientific Computation Rua Getulio Vargas 333 Quitandinha-Petrópolis 25651-070 Rio de Janeiro RJ Brazil 3 CI2MA and Departamento de Ingeniería Matemứtica Universidad de Concepción Casilla 160-C 4070386 Concepcion Chile 4 Departamento de Matemdtica Universidad del Bío-Bío Collao 1202 Casilla 5-C 4081112 Conception Chile Correspondence should be addressed to Mauricio Sepulveda mauricio@ Received 24 November 2010 Accepted 17 February 2011 Academic Editor Wenming Zou Copyright 2011 Margareth S. Alves et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We show that the energy to the thermoelastic transmission problem decays exponentially as time goes to infinity. We also prove the existence uniqueness and regularity of the solution to the system. 1. Introduction In this paper we deal with the theory of thermoelasticity. We consider the following transmission problem between two thermoelastic materials piutt - p1 Au - p1 11 V div u - m1VỠ 0 in Q1 X 0 to p2vtt - p2Av - p2 12 V divv - m2ve 0 in Q2 X 0 to T10t - k1AỠ - m1 div ut 0 in Q1 X 0 to T2dt - K2AQ - m2 div vt 0 in Q2 X 0 to . 2 Boundary Value Problems Figure 1 Domains Q1and Q2 and boundaries of the transmission problem. We denote by x x1 . xn a point of Qi i 1 2 while t stands for the time variable. The displacement in the thermoelasticity parts is denoted by u Q1 X 0 x R u u1 . . un Ui ui x t i 1 . ri and V Q2 X 0 x R V v1 . . vn Vi Vi x t i
