Existence Of Solution For A Fourth-order Parabolic Equation

In this thesis,we study the initial-boundary value problem for a four-order parabolic equation ut+?2u =?div(|u|m(?)u),x ??,t ?(0,T),(?)u/(?)r =(?)?u/(?)n= 0,X?(?)?,t ?(0,T),u(x,0)= u0(x),X??,where ?(?)RN(n? 2)is a bounded domain,with smooth boundary(?)? and ?>0 is a constant.Using Kato's method,we establish the existence,uniqueness and regularity of the solu-tion to the model,in suitable spaces,namely C0([0,T];Lp(?))where p = n(m+1)/2,with m>0,n ? N,and n ? 2.We also show the global existence solution to the nonlinear parabolic equation for small initial data.Our main tools are Lp-Lq estimates,regularization property of linear part of e-t?2 and successive approximations.