Existence Of Radial Solutions For A Class Of The Sixth-order Parabolic Equations With Nonlinear Diffusion Term

In this thesis,we consider the following sixth-order parabolic equation with initial boundary conditions,(?),where ? is the unit ball in R~2,f(u)is a nonnegative function,and v is the unit normal to ??.The equation is a typical sixth-order thin film equation,which has a sharp physical background and a rich theoretical connotation.It is derived from the isolation oxidation of silicon for industrial applications.Notice that the actual model for the motion of oil film spreading over a solid surface occurs in two-dimensional space.To describe the motion,we should consider the problem in higher dimensional spaces.Based on the Schauder type estimates,we establish the global existence of classical solutions for regularized problems.After establishing some necessary uniform estimates on the approximate solutions,we prove the existence of radial solutions.