关键词: 非散度型, 非线性抛物方程组, Cauchy问题, 爆破, 局部化

Abstract: Some properties of the solutions of the Cauch y problem for a class of nonlinear parabolic systems, in non-divergence form, w ere studied. Under different conditions, a series of global solutions and a seri es of blowup solutions of the system were constructed; on the other hand, it is proved that under some conditions, any weak solution of the problem possesses t he localization property which generalizes an important result in reference.

Key words: non-divergence form, nonlinear parabolic system, Cauc hy problem, blowup, localization