naa a22 4500 510812295 CHVBK 20180411083448.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1134/S0081543813040172 doi (NATIONALLICENCE)springer-10.1134/S0081543813040172 Chugainova A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut Nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation [Elektronische Daten] [A. Chugainova] Nonstationary solutions of the Cauchy problem are found for a model equation that includes complicated nonlinearity, dispersion, and dissipation terms and can describe the propagation of nonlinear longitudinal waves in rods. Earlier, within this model, complex behavior of traveling waves has been revealed; it can be regarded as discontinuity structures in solutions of the same equation that ignores dissipation and dispersion. As a result, for standard self-similar problems whose solutions are constructed from a sequence of Riemann waves and shock waves with stationary structure, these solutions become multivalued. The interaction of counterpropagating (or copropagating) nonlinear waves is studied in the case when the corresponding self-similar problems on the collision of discontinuities have a nonunique solution. In addition, situations are considered when the interaction of waves for large times gives rise to asymptotics containing discontinuities with nonstationary periodic oscillating structure. Pleiades Publishing, Ltd., 2013 Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 204-212 0081-5438 281:1<204 2013 281 11501 https://doi.org/10.1134/S0081543813040172 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813040172 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chugainova A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 204-212 0081-5438 281:1<204 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer