Differential equations and Optimal control

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

E. V. Ustilko, F. E. Lomovtsev

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract: 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.

Keywords: mixed problem; characteristic first oblique derivative; initial conditions; smoothness requirements; matching conditions.

UDC: 517.956.32

DOI: 10.33581/2520-6508-2020-1-30-37