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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.
Citation:
E. V. Ustilko, F. E. Lomovtsev, “Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation”, Journal of the Belarusian State University. Mathematics and Informatics, 1 (2020), 30–37
Linking options:
https://www.mathnet.ru/eng/bgumi49 https://www.mathnet.ru/eng/bgumi/v1/p30
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Abstract page: | 55 | Full-text PDF : | 30 | References: | 14 |
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