Open AccessСlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition
Author(s) -
В. И. Корзюк,
Я. В. Рудько
Publication year - 2020
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2020-64-6-657-662
Subject(s) - uniqueness , mathematics , mathematical analysis , boundary value problem , discontinuity (linguistics) , piecewise , initial value problem , cauchy boundary condition , plane (geometry) , boundary (topology) , wave equation , mixed boundary condition , cauchy problem , boundary problem , geometry
In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.