Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation

• Main Authors: Ekaterina V. Ustilko, Fiodar E. Lomovtsev
• Format: Article
• Language: Belarusian
• Published: Belarusian State University 2020-03-01
• Series: Журнал Белорусского государственного университета: Математика, информатика
• Subjects: mixed problem; characteristic first oblique derivative; initial conditions; smoothness requirements; matching conditions
• Online Access: https://journals.bsu.by/index.php/mathematics/article/view/1098

Sufficient matching conditions the time-dependent characteristic first derivatives in the boundary mode with the initial conditions and the more general vibration equation of a semi-bounded string are derived in the sets of solutions of all higher order smoothness orders. They generalize the previously found sufficient matching conditions in the case of a similar mixed problem for the simplest string vibration equation. The characteristic of non-stationary first oblique derivatives in the boundary mode means that at each moment of time they are directed along the critical characteristic.