Open AccessMixed problem for a one-dimensional wave equation with conjugation conditions and second-order derivatives in boundary conditions
Author(s) -
В. И. Корзюк,
С. Н. Наумовец,
В. П. Сериков
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-3-287-297
Subject(s) - boundary value problem , mathematics , mathematical analysis , homogeneous , mixed boundary condition , separation of variables , boundary (topology) , order (exchange) , cauchy boundary condition , function (biology) , free boundary problem , boundary problem , cauchy problem , initial value problem , finance , combinatorics , evolutionary biology , economics , biology
In this paper, we consider the boundary problem for the half-strip on the plane for the case of two independent variables. This mixed problem is solved for a one-dimensional wave equation with Cauchy conditions on the basis of the half-strip and boundary conditions for lateral parts of the area border containing second-order derivatives. Moreover, the conjugation conditions are specified for the required function and its derivatives for the case when the homogeneous matching conditions are not satisfied. A classical solution to this problem is found in an analytical form by the characteristics method. This solution is approved to be unique if the relevant conditions are fulfilled.