Geodesic
Method of perturbations in boundary value problems of impact deformation of incompressible elastic mediums
Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 1, pp. 71-77 
Yu. E. Ivanova; V. E. Ragozina. Method of perturbations in boundary value problems of impact deformation of incompressible elastic mediums. Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 1, pp. 71-77. http://geodesic.mathdoc.fr/item/DVMG_2003_4_1_a7/
@article{DVMG_2003_4_1_a7,
     author = {Yu. E. Ivanova and V. E. Ragozina},
     title = {Method of perturbations in boundary value problems of impact deformation of incompressible elastic mediums},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {71--77},
     year = {2003},
     volume = {4},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2003_4_1_a7/}
}
TY  - JOUR
AU  - Yu. E. Ivanova
AU  - V. E. Ragozina
TI  - Method of perturbations in boundary value problems of impact deformation of incompressible elastic mediums
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2003
SP  - 71
EP  - 77
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2003_4_1_a7/
LA  - ru
ID  - DVMG_2003_4_1_a7
ER  - 
%0 Journal Article
%A Yu. E. Ivanova
%A V. E. Ragozina
%T Method of perturbations in boundary value problems of impact deformation of incompressible elastic mediums
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2003
%P 71-77
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2003_4_1_a7/
%G ru
%F DVMG_2003_4_1_a7

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

On an example of a solution of the one-dimensional task with a rotational symmetry about antiflat impact loading of an incompressible elastic medium till it cylindrical boundary surface the singularities are considered informations of the similar tasks to the singular tasks of a method of perturbations. The recurrent solutions of nonlinear developmental the equations, implying at sequential application of developed variant of a method of perturbations, appear as interior expansion near to wave front.

[1] A. A. Burenin, V. A. Sharuda, “Odnomernyi perekhodnyi volnovoi protsess deformatsii pri udarnom nagruzhenii uprugogo poluprostranstva”, Izv. AN SSSR. Mekhanika tverdogo tela, 1984, no. 1, 40–44

[2] A. A. Burenin, V. A. Sharuda, “Kosoi udar po uprugomu poluprostranstvu”, Izv. AN SSSR. Mekhanika tverdogo tela, 1984, no. 6, 172–177

[3] A. A. Burenin, Yu. A. Rossikhin, “K resheniyu odnomernoi zadachi nelineinoi dinamicheskoi teorii uprugosti so strukturnoi udarnoi volnoi”, Prikladnaya mekhanika, 26:1 (1990), 103–108 | MR | Zbl

[4] A. A. Burenin, V. E. Ragozina, “O prifrontovykh asimptotikakh v nelineinoi dinamicheskoi teorii uprugosti”, Problemy mekhaniki sploshnykh sred i elementov konstruktsii, k 60-letiyu professora G. I. Bykovtseva, Dalnauka, Vladivostok, 1998, 225–240

[5] Chy Boa-Teh, “Finite amplitude waves in incompressible elastic solids”, J. Mech. Phys. Solids., 15:1 (1967), 1–14 | DOI

[6] A. A. Burenin, “Ob udarnom deformirovanii neszhimaemogo uprugogo poluprostranstva”, Prikladnaya mekhanika, 21:5 (1985), 3–8 | Zbl

[7] A. Kh. Naife, Metody vozmuschenii, Mir, M., 1976, 445 pp. | MR