Study Of Solutions To A Fourth Order Viscous Degenerate Parabolic Equation With Diffusion Term

This thesis deals with the existence and uniqueness for a class of fourth-order parabolic equation.The substantial difficulty is that the maximum principle does not hold again and so we need to apply the energy estimate method to give the existence of weak solutions.Chapter 1 is devoted to showing the background and development of the fourth order parabolic equation recently.Chapter 2 is devoted to studying the initial boundary value problem of a fourth order viscous degenerate parabolic equation with a linear diffusion term:Under some assumptions on the initial value,by using the time discretization method,the minimizers functional method,the poincare inequality and young inequality,the existence of a discrete problem is proved.Moreover,by constructing the approximation solutions of the degenerate parabolic equation,the necessary uniform estimates are obtained and then we can gain the convergence results.Finally,the existence of the weak solutions is proved.Chapter 3 is to study initial boundary value problem of fourth-order degenerate parabolic equation in high dimensional spaceThe equation has been widely applied in biological population,pollen and fluid diffusion etc.This chapter is mainly concerned with the effect of the linear diffusion,which can be better to describe the background of the corresponding model.We also take the semi-discrete method to study its existence.By constructing some approximation solutions by the existence of the corresponding elliptic equation,the existence and uniqueness of weak solutions of the parabolic problem is obtained.