Global Existence Of Small Amplitude Solutions Of The Cauchy Problem For The Generalized Bq Equations With Damped Term

This paper consists of four chapters. The first chapter is the introduction, which will give the physical meaning and research results of the equation. The second chapter will give the notations and inequalities. In the third chapter, we will study the large time behavior of solutions to the cauchy problem for the generalized Boussinesq(Bq) equations with damped term First of all, applying the Fourier transformation and the Duhamel principle, the Cauchy problem for the linear Boussinesq(Bq) equation is written an equivalence integral equa-tion. What’s more, applying symbolic analysis methods we establish the decay estimate and existence of the solution to the linear Boussinesq(Bq) equation. Finally using the contraction mapping principle and integral estimates we give the existence and uniform decays of the cauchy problem of the generalized Boussinesq(Bq) equation in the case that the initial data are small.