tailieunhanh - báo cáo hóa học:" Research Article Exponential Stability and Global Attractors for a Thermoelastic Bresse System"

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 Exponential Stability and Global Attractors for a Thermoelastic Bresse System | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 748789 15 pages doi 2010 748789 Research Article Exponential Stability and Global Attractors for a Thermoelastic Bresse System Zhiyong Ma College of Science Shanghai Second Polytechnic University Shanghai 201209 China Correspondence should be addressed to Zhiyong Ma mazhiyong1980@ Received 13 September 2010 Accepted 29 October 2010 Academic Editor E. Thandapani Copyright 2010 Zhiyong Ma. 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 consider the stability properties for thermoelastic Bresse system which describes the motion of a linear planar shearable thermoelastic beam. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations. We use multiplier techniques to prove the exponential stability result when the wave speed of the vertical displacement coincides with the wave speed of the longitudinal or of the shear angle displacement. Moreover the existence of the global attractor is firstly achieved. 1. Introduction In this paper we will consider the following system phw1tt Eh w1x - kw3 - a01t x - kGh ộ2 w3x kw1 phw3tt Gh ệ2 W3x kW1 x kEh W1x - kw3 - ka01t pIỘ2tt EIỘ2xx - Gh 2 W3x kW1 - ad3x pc01tt 01xxt 01xx - aT0 w1tx - kwat pc03t 03xx - ÓTữộĩtx together with initial conditions w1 x 0 uo x Ộ2t x 0 c x 01 x 0 00 x W1t x 0 Vo x W3 x 0 Wq x 01t x 0 no x Ộ2 x 0 Ộq x W3t x 0 q x 03 x 0 x 2 Advances in Difference Equations and boundary conditions w1 x t w3x x t ộ2 x t 01 x t 03 x t 0 for x 0 1 where w1 w3 and ộ2 are the longitudinal vertical and shear angle displacement 01 and Ỡ3 are