拟线性正对称方程组的边值问题及其对混合型方程的应用

<正> 1.引言 本文有两个目的.第一个目的是讨论拟线性正对称方程组的边值问题.如所知,线性的正对称方程组是一类相当广泛的偏微分方程组,许多常见的偏微分方程都可以化为正对称方程组去.对于这个方程组,可以利用能量不等式来证明许多边值问题的适定性.本文充分利用线性正对称方程组的结果,经过适当的估计,用压缩映照原理证明了拟线性正对称方程组的边值问题的解的存在性.对求解的区域而言,问题是大范围的,但

BOUNDARY VALUE PROBLEMS FOR QUASILINEAR POSITIVE SYMMETRIC SYSTEMS AND THEIR APPLICATIONS TO MIXED EQUATIONS

The theory of linear symmetric positive systems of PDE is extended to the quasilinear ease. An existence theorem for a large elass of boundary value problems is established provided the systems are sufficiently positive. Using this theorem we prove the existences of solutions of some boundary problems for a certain class of 2nd order quasilinear mixed PDE with n independent variables. The equations can not be linealized by any known transformation and the elliptie regions and hyperbolie regions can not be identified before the solutions are determined.