Geodesic
Asymptotic behavior of nonlinear waves in elastic media with
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 240-256

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: nonlinear hyperbolic equations, shock waves, dissipation
Mots-clés : dispersion. 
A. P. Chugainova. Asymptotic behavior of nonlinear waves in elastic media with. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 240-256. http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a2/
@article{TMF_2006_147_2_a2,
     author = {A. P. Chugainova},
     title = {Asymptotic behavior of nonlinear waves in elastic media with},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {240--256},
     year = {2006},
     volume = {147},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a2/}
}
TY  - JOUR
AU  - A. P. Chugainova
TI  - Asymptotic behavior of nonlinear waves in elastic media with
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 240
EP  - 256
VL  - 147
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a2/
LA  - ru
ID  - TMF_2006_147_2_a2
ER  - 
%0 Journal Article
%A A. P. Chugainova
%T Asymptotic behavior of nonlinear waves in elastic media with
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 240-256
%V 147
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a2/
%G ru
%F TMF_2006_147_2_a2

[1] A. G. Kulikovskii, DAN SSSR, 275:6 (1984), 1349–1352 | MR

[2] A. G. Kulikovskii, A. P. Chugainova, ZhVMiMF, 44:6 (2004), 1119–1126 | MR | Zbl

[3] A. G. Kulikovskii, N. I. Gvozdovskaya, Tr. MIAN, 223, 1998, 63–73 | MR | Zbl

[4] A. G. Kulikovskii, E. I. Sveshnikova, Nelineinye volny v uprugikh sredakh, Mosk. litsei, M., 1998

[5] A. G. Kulikovskii, N. V. Pogorelov, A. Yu. Semenov, Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | MR | Zbl

[6] N. S. Bakhvalov, M. E. Eglit, Dokl. RAN, 370:1 (2000), 1–4 | MR | Zbl

[7] A. A. Samarskii, Yu. P. Popov, Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1978 | MR | Zbl