二元混合型偏微分方程的Frankl问题和Tricomi问题  

The Relationship of the Frankl Problem and Tricomi Problem for a Mixed Equation of Second Order

作　　者：岳松[1] 

机构地区：[1]复旦大学数学科学学院,上海200433

出　　处：《复旦学报（自然科学版）》2012年第4期437-449,共13页Journal of Fudan University：Natural Science

摘　　要：研究一个二元混合型偏微分方程的Frankl问题解的存在惟一性,并讨论此方程的Frankl问题的解如何趋向于其对应的Tricomi问题的解.此混合型方程的系数在双曲型区域与椭圆型区域的连接线上是间断的.主要结果是:此方程的Frankl问题在H1中存在惟一的解;当Frankl问题的边界条件给法趋向于Tricomi问题的边界条件给法时,该方程的Frankl问题的解也在H1中趋近于其对应的Tricomi问题的解.The unique existence of the solution of the Frankl problem and the relationship of the Frankl problem and Tricomi problem for a mixed equation of second order are studied.The coefficients of the equation are discontinuous on the connection line of the elliptic domain and the hyperbolic domain.The main results are the unique existence of the solution of the Frankl problem and that the solution of the Frankl problem converges to the solution of the Tricomi problem in H1 when the setting of the boundary conditions of the Frankl problem approaches that of the Tricomi problem.

关 键 词：混合型方程 Frankl问题 TRICOMI问题 黎曼函数 

分 类 号：O175.25[理学—数学] O175.27[理学—基础数学]