Global Existence Of Smooth Solutions Of Cauchy Problem For Timoshenko Equations And Bipolar Non-isentropic Euler-poisson Equations

The global existence of smooth solutions of the Cauchy problem for Timoshenko equations and the periodic region problem of bipolar non-isentropic Euler-Poisson equa-tions is studied.For Timoshenko equations,it is transformed into general symmetric hyperbolic equations.Under the Sobolev space framework,the energy estimates of the solutions and the dissipation energy estimates of the corresponding variables are ob-tained by using the energy integral method and the anti-symmetry technique.The global existence of solutions closing to constant equilibrium states is obtained by con-tinuous extension method.For the bipolar Euler-Poisson equations,the parameter of relaxation time ??(0,1]is included in the equations.We obtain the uniform global existence result of the smooth solution for this parameter ? ?(0,1]with establishing the uniform energy estimates of the parameter.The structure of the paper is organized as follows:In chapter one,firstly,the research progress of Timoshenko equations and Euler-Poisson equations in recent years and the significance of this paper are introduced.Secondly,the main results of this paper are described.In chapter two,some classical inequalities are introduced.In chapter three,we prove the global existence of smooth solutions of Cauchy problem for Timoshenko equations,that is,theorem 1.1 is proved.In chapter four,for bipolar non-isentropic Euler-Poisson equations,the uniform energy estimates with parameter ? are established,and the global existence of the smooth solutions for parameter ? is obtained,which proves theorem 1.2.