一阶混合型方程组的间断边值问题  

DISCONTINUOUS BOUNDARY VALUE PROBLEMS FOR FIRST ORDER SYSTEMS OF MIXED TYPE

作　　者：闻国椿[1] 杨丕文[2] 

机构地区：[1]北京大学数学系,北京100871 [2]四川师范大学数学系,成都610066

出　　处：《系统科学与数学》2001年第2期243-249,共7页Journal of Systems Science and Mathematical Sciences

摘　　要：本文论讨单连通区域上一阶线性混合型（椭圆一双曲型）方程组的间断边值问题．我们首先给出混合型方程组特别是最简单的混合型方程组解的表示式，然后使用逐次逼近法，证明上述边值问题解的存在性与唯一性．由以上结果，可导出Ａ．Ｖ．Ｂｉｔｓａｄｚｅ所得的Ｌａｖｒｅｎｔ’ｅｖ－Ｂｉｔｓａｄｚｅ方程：ｕｘｘ＋ｓｇｎｙｕｙｙ＝０的Ｔｒｉｃｏｍｉ问题的可解性．This paper deals with discontinuous boundary value problems for first order linear systems of mixed (elliptic-hyperbolic) type equations in a simply connected domain. Firstly, we derive the representation of solutions of the above boundary value problems for the mixed system, and then by using the method of successive iteration, the existence and uniqueness of solutions for the above problems are proved. From these results, we can derive the result on the Thicomi problem for Lavrent'ev-Bitsadze equation uxx+sgnyuyy =0 obtained by A. V. Bitsadze.

关 键 词：间断边值问题 线性混合型方程组 一阶 连通区域 解 逐次逼近法 Lavrent'ev-Bitsadze方程 TRICOMI问题 

分 类 号：O175.8[理学—数学] O175.28[理学—基础数学]