一类非散度型非线性抛物方程组Cauchy问题解的性质

Some Properties of Solutions for a Class of Nonlinear Parabolic Systems in Non-divergence Form

研究一类非散度型非线性抛物方程组Cauchy问题解的性质.在不同条件下,构造了此方程组一系列整体解与一系列爆破解;在某些条件下,证明了这个问题的弱解具有局部化性质,从而推广了已有文献中的一些结果.

Some properties of the solutions of the Cauchy problem for a class of nonlinear parabolic systems, in non-divergence form, were studied. Under different conditions, a series of global solutions and a series 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 the localization property which generalizes an important result in reference.