Open AccessThe third boundary problem for the hyperbolic differential equation of the second order
Author(s) -
G N Shevchenko,
A Yu Borisenko
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1902/1/012046
Subject(s) - mathematics , hyperbolic partial differential equation , mathematical analysis , boundary value problem , third order , homogeneous , boundary (topology) , partial differential equation , elliptic partial differential equation , free boundary problem , order (exchange) , homogeneous differential equation , first order partial differential equation , series (stratigraphy) , differential equation , ordinary differential equation , combinatorics , differential algebraic equation , philosophy , paleontology , theology , finance , economics , biology
This article consider the solvability of the problem for the model linear homogeneous differential equation with partial derivatives of the second order of hyperbolic type on the plane in the square for the case of discontinuous conjugation conditions on the characteristics with the third series boundary conditions on the whole boundary of the region under consideration. Dalamber’s solution is used for this problem solving. The conditions for the single-valued solvability of the defined problem are clarified in this paper. As a result, an exact solution was obtained in an explicit form.