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INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR PARABOLIC SYSTEM OF FOURTH-ORDER
陈国旺
数学物理学报(英文版). 1991 (4):
393-400.
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.
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