INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR PARABOLIC SYSTEM OF FOURTH-ORDER

In this paper, the periodic boundary problem and the initial value problem for the nonlinear system of parabolic type u1=-A（x, t）ux4+B（x, t）ux2+（g（u））x2+（grad h（u））x+f（u）are studied, where u（x, t）=(u1（x, t）.…, uJ（x, t） is a J-dimensional unknown vector valued function, f（u） and g（u） are the J-dimensional vector valued function of u（x, t）, h（u） is a scalar function of u, A（x, t） and B（x, t） are J×J matrices of functions. The existent, uniqueness and regularities of the generalized global solution and classical global solution of the problems are proved. When J=1, h（u）=0, g（u）=au3, A=a1, B=a2, where a1, a2 a are constants, the system is a generalized diffusion model equation in population problem.