Blow-up Of Two Classes Generalized Boussinesq Equations With Arbitrary High Initial Energy

Nonlinear Partial Differential Equation is an important branch of modern mathematics,Nonlinear Partial Differential Equations are used to describe the issues which in theory and practice such as mechanics,control processes,ecological and economic systems,chemical cycle systems and epidemiology.The Nonlinear Partial Differential Equation is used to describe the above problems with full consideration of space and time,the influence of time delay,so it is accurately to reflect the reality.Many scholars have invested a lot of effort in their research.The blow-up results of Nonlinear Partial Differential Equations have become one of the most important research topics.Especially in recent years,more and more scholars have begun to interest in the Boussinesq equation,which is applied to describe the phenomenon of long-wave motion with small amplitude,it is frequently used to water wave motion in shallow seas and seaports in model experiment,and it is widely used to marine engineering.In this thesis,we mainly study the Cauchy problem for generalized Boussinesq equation with double damping terms.In section 1,we provide some research status,physical background and various kinds of results of the researchers about the Boussinesq equation,furthermore we provide the research status of the Boussinesq equation with damping term,what's more we give main systems of this paper.Through the introduction of these basic information,there is a framework and interest in reading.In section 2,we consider the Cauchy problem of the generalized Boussinesq equation with double damping terms.By using improved convexity method combined with potential well method and Fourier transform,we show the finite time blow-up of the solution with arbitrarily high initial energy while many similar results require the corresponding energy to be less than some certain numbers.In section 3,We study the Cauchy problem of the six-order high-dimensional generalized Boussinesq equation with double damping terms.By using improved convexity method combined with Fourier transform,we show the finite time blow-up of solution with arbitrarily high initial energy.