On the existence and uniqueness of a generalized solution of the Protter problem for (3+1)-D Keldysh-type equations

被引：0

作者：

Popivanov, Nedyu ^{[1
]}

Hristov, Tsvetan ^{[1
]}

Nikolov, Aleksey ^{[2
]}

Schneider, Manfred ^{[3
]}

机构：

[1] Univ Sofia, Fac Math & Informat, Sofia 1164, Bulgaria

[2] Tech Univ Sofia, Fac Appl Math & Informat, Sofia 1000, Bulgaria

[3] Karlsruhe Inst Technol, Fac Math, D-76131 Karlsruhe, Germany

来源：

BOUNDARY VALUE PROBLEMS | 2017年

关键词：

weakly hyperbolic equations; boundary value problems; generalized solutions; uniqueness; behavior of solution; BOUNDARY-VALUE-PROBLEMS; SINGULAR SOLUTIONS; NONTRIVIAL SOLUTIONS; DARBOUX PROBLEM; LINE;

D O I：

10.1186/s13661-017-0757-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A (3 + 1)-dimensional boundary value problem for equations of Keldysh type (the second kind) is studied. Such problems for equations of Tricomi type (the first kind) or for the wave equation were formulated by M.H. Protter (1954) as multidimensional analogues of Darboux or Cauchy-Goursat plane problems. Now, it is well known that Protter problems are not correctly set, and they have singular generalized solutions, even for smooth right-hand sides. In this paper an analogue of the Protter problem for equations of Keldysh type is given. An appropriate generalized solution with possible singularity is defined. Results for uniqueness and existence of such a generalized solution are obtained. Some a priori estimates are stated.

引用

页数：30

共 52 条

[1] A criterion for the existence of eigenfunctions of the Darboux-Protter spectral problem for degenerating multidimensional hyperbolic equations [J].