Open AccessThe classical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition
Author(s) -
V. I. Korzyuk,
J. V. Rudzko
Publication year - 2021
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2021-57-1-23-32
Subject(s) - mathematics , uniqueness , mathematical analysis , boundary value problem , initial value problem , discontinuity (linguistics) , cauchy boundary condition , piecewise , mixed boundary condition , cauchy problem , wave equation , boundary problem , boundary (topology)
In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom of the boundary, the Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at a point. The smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved, and the conditions under which a piecewise-smooth solution exists are established. The problem with conjugate conditions is considered