【摘要】 <正> Friedrichs,K.O.,Lax,P.D.等人所建立的一阶正对称方程组理论在国内有不少研究。这些工作沿着两个不同的方向,一个方向是将高阶方程(例如混合型方程)定解问题化成一阶正对称方程组进行研究。另一方向是推广Friedrichs-Lax理论到高阶,用以直接研究高阶方程的定解问题。本文将研究高阶方程与一阶正对称方程组的关系。更多还原

【Abstract】 In this paper we study the relation between symmetric positivo systems and equations of higher order. The main result is:Theorem 1. An equation of second order LΦ=f can be transfromed into a symmetric positive system by introducing new unknown functionsu_i=sum from j=0 to n (a_ijφ_j（i=0, 1, …, n）), φ₀=φ, φ_j=（（?）φ）/（（?）x_j） iff there exists L₁ of order 1 such thatRe(L₁φ·（?）=sum from i=1 to n （（?）P_i（φ, φ）+B（φ, φ））, where P_i（φ, φ）（i=1, …, n）, B（φ, φ）are differential quadartic froms and B（φ, φ） is positive definite.This Theorem can be extended into equations of higher order.Some examples of deducing equations of higher order into symmetric positive systems are given.Finally, we give a counter example which shows that a boundary problem of a symmetric positive system deduced from an equation of higher order is admissible, but its corresponding bounbary problem of the original equation is not well-posed.更多还原