Riemann-Hadamard method for solving a (2+1)-D problem for degenerate hyperbolic equation

作     者：Aleksey Nikolov Nedyu Popivanov 

作者机构：1Department of Applied Mathematics and Informatics Technical University of Sofia 1000 Sofia Bulgaria 2Department of Mathematics and Informatics University of Sofia 1164 Sofia Bulgaria 

出 版 物：《AIP Conference Proceedings》 

年 卷 期：2015年第1690卷第1期

学科分类：07[理学] 0702[理学-物理学] 

摘      要：We consider a (2+1)-D boundary value problem for degenerate hyperbolic equation, which is closely connected with transonic fluid dynamics. This problem was introduced by Protter in 1954 as a multi-dimensional analogue of the Darboux problem in the plain, which is known to be well-posed. However the (2+1)-D problem is overdetermined with infinitely many conditions necessary for its classical solvability and there exist generalized solutions of this problem with strong *** years we study the exact asymptotic behavior of such singular solutions. We offer a Riemann-Hadamard method for solving the problem instead of the used until now method of successive approximations for solving an equivalent integral equation. As result, we obtain a more convenient representation of the singular solutions giving more precise results in our investigation.