The Global Attractor For A Class Of Hypebolic Of The Coupling Rod With Nonlinear Heat Source Term

Partial differential equations, one of the most active branch of mathematics, is the foundation of mathematics and physics in a lot of content and extensive contacts with other branches of science. With the merging of the classic and the modem, it forms a huge system and get numerous applications in elastic mechanics, electricity and magnetism, quantum mechanics, economics and so on. The studying of the existence and uniqueness of the solution and global attractors is the focus of attention, especially the initial boundary value problem of second order differential equations.This paper studies the dynamic behavior of the partial differential equations of second order nonlinear hyperbolic equations to investigate the existence and uniqueness of the solution and the existence of global attractors of the dynamical system from the elastic mechanics, which coupling lever system with a strong damping of thermal effects. Initial conditions u(x,0)=u0(x), ut(x,O)=u1(x), θ(x,0)=θ0(x), x∈Ω Boundary conditions u(x,t)|x∈(?)Ω=0, θ(x,t)|x∈(?)Ω=0, t≥0Where α,γ is constant greater than0.The full text is divided into five chapters:The first chapter mainly explains the research background, the achievement and the status, and then illustrated the main content of this paper.The second chapter describes related underlying concepts such as the global attractor, absorbing set, sectorial operators, semigroups of operators, esc and gives some basic theorem, lemma associated with global attractor.The third chapter studies of a class of initial boundary value problem of coupled rod system with a nonlinear heat source term. Using the classical operator semigroup theory proves the existence, uniqueness and continuity of the solution.The fourth chapter proves the existence of the global attractors of the system, using the classical method of semigroups decomposition.The fifth chapter, concluding this article and prospects of researches are presented.