系数允许间断的拟线性抛物方程组的逐片古典解

The Global Piecewise Classical Solutions for Quasilinear Parabolic Systems with Discontinuous Coefficients

利用上下解方法和估计,研究了系数允许间断的n维拟线性弱耦合抛物方程组。所研究的方程的主部允许不同,并且向量反应函数是混拟单调的。文章的目的是得到整体的逐片古典解的存在性唯一性。

The n - dimensional weakly coupled quasilinear parabolic systems with discontinuous coefficients is investigated by the method of upper and lower solutions and various estimates. The principal parts of the equations are allowed to be different, and the vector reaction function is mixed quasimonotone. The goal of this paper is to show the exis ence and uniqueness of the global piecewise classical solutions.