caa a22 4500 467911576 CHVBK 20180406152850.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s11232-006-0067-8 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0067-8 Chugainova A. Steklov Mathematical Institute, RAS, Moscow, Russian aut Asymptotic behavior of nonlinear waves in elastic media with dispersion and dissipation [Elektronische Daten] [A. Chugainova] In the case of nonlinear elastic quasitransverse waves in composite media described by nonlinear hyperbolic equations, we study the nonuniqueness problem for solutions of a standard self-similar problem such as the problem of the decay of an arbitrary discontinuity. The system of equations is supplemented with terms describing dissipation and dispersion whose influence is manifested in small-scale processes. We construct solutions numerically and consider self-similar asymptotic approximations of the obtained solution of the equations with the initial data in the form of a "spreading” discontinuity for large times. We find the regularities for realizing various self-similar asymptotic approximations depending on the choice of the initial conditions including the dependence on the form of the functions determining the small-scale smoothing of the original discontinuity. Springer Science+Business Media, Inc., 2006 nonlinear hyperbolic equations nationallicence shock waves nationallicence dissipation nationallicence dispersion nationallicence Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 646-659 0040-5779 147:2<646 2006 147 11232 https://doi.org/10.1007/s11232-006-0067-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0067-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chugainova A. Steklov Mathematical Institute, RAS, Moscow, Russian aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 646-659 0040-5779 147:2<646 2006 147 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer