Pullback Attractors For A Class Of Wave Equations On Unbounded Domains

Pullback attractor is compact set which describe the long time behavior of solutions,It is an important tool to study the infinite dimensional dynamical system.This paper consider pullback attractors for a class of wave equation on unbounded domains,get the existence of pullback attractors for nonautonomous BrinkmanForchheimer equation on unbounded domain and nonautonomous Sine-Gordon equation.The full text is divided into five chapters.The first chapter introduce the background of infinite dimensional dynamical systems and show the development and research for global attractors,uniform attractor and pullback attractor in autonomous and nonautonomou case.Moreover,This Chapter introduce the main problem and ideas discussed in this paper.The second chapter introduce the prepare konwledge of the reaearch problem,give some relevant symbols,inequalities,theorem and related theory which preparing for the following discussion.The third chapter studies pullback attractor for nonautonomous Brinkman Forchheimer equation on unbounded domain.The sobolev embedded on unbounded domain is no longer tight.This seation using cut-off function and tail estimate method to proved the existence of pullback attractor on unbounded domain.The space is divided into two parts,bounded and unbounded.This chapter using sobolev embedded on bounded domain.Moreover,the index is decayed to zero on unbounded part.The fourth chapter studies pullback attractor for nonautonomous Sine-Gordon equation on unbounded domain,in the same way,embedded no longer tight at this time,we first estimate the solution of this equation.This chapter proved that the existence of pullback attractor absorbing set by solving the consistent estimate of the result.we construct the energy equation prove asymptotic compactness,then get pullback attractor for nonautonomous Sine-Gordon equation on unbounded domain.The fifith chapter summary that this paper and prospects of research on pullback attractor.