Geodesic
The evolutionary equation for wave processes of the shift deformation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 14-24.

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

One-dimensional process of formation and the subsequent motion of a flat cross shock wave is studied on the basis of solutions of the corresponding nonlinear evolutionary equation. This equation defines behaviour of the solution in front area of wave process and follows from interior lines of a method of matched asymptotic expansions. Comparative transient analysis of strains of a deformation and volume will be carried out and their basic differences are specified. In the capacity of model examples solutions of some concrete boundary value problems of a dynamic shift straining are observed. 
@article{ISU_2009_9_4_a2,
     author = {A. A. Burenin and V. E. Ragozina and Yu. E. Ivanova},
     title = {The evolutionary equation for wave processes of the shift deformation},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {14--24},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a2/}
}
TY  - JOUR
AU  - A. A. Burenin
AU  - V. E. Ragozina
AU  - Yu. E. Ivanova
TI  - The evolutionary equation for wave processes of the shift deformation
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2009
SP  - 14
EP  - 24
VL  - 9
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a2/
LA  - ru
ID  - ISU_2009_9_4_a2
ER  - 
%0 Journal Article
%A A. A. Burenin
%A V. E. Ragozina
%A Yu. E. Ivanova
%T The evolutionary equation for wave processes of the shift deformation
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2009
%P 14-24
%V 9
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a2/
%G ru
%F ISU_2009_9_4_a2
A. A. Burenin; V. E. Ragozina; Yu. E. Ivanova. The evolutionary equation for wave processes of the shift deformation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 4, pp. 14-24. http://geodesic.mathdoc.fr/item/ISU_2009_9_4_a2/

[1] Gelfand I. M., “Nekotorye zadachi teorii kvazilineinykh uravnenii”, Uspekhi mat. nauk, 14:2 (1959), 87–158 | MR | Zbl

[2] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya v gazovoi dinamike, Nauka, M., 1978, 688 pp. | MR

[3] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977, 622 pp. | MR

[4] Pelinovskii Yu. N., Fridman V. E., Engelbrekht Yu. K., Nelineinye evolyutsionnye uravneniya, Valgus, Tallin, 1984, 164 pp. | MR

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

[6] Burenin A. A., Rossikhin Yu. A., “Luchevoi metod resheniya odnomernykh zadach nelineinoi dinamicheskoi teorii uprugosti s ploskimi poverkhnostyami silnykh razryvov”, Prikladnye zadachi mekhaniki deformiruemykh sred, DVO AN SSSR, Vladivostok, 1991, 129–137

[7] Sedov L. I., Mekhanika sploshnoi sredy, v. 1, 2, 2-e izd. ispr. i dop., Nauka, M., 1973

[8] Tomas T., Plasticheskoe techenie i razrushenie v tverdykh telakh, Mir, M., 1964, 308 pp.

[9] Kulikovskii A. G., Sveshnikova E. I., Nelineinye volny v uprugikh sredakh, Moskovskii litsei, M., 1998, 412 pp.

[10] Koul Dzh., Metody vozmuschenii v prikladnoi matematike, Mir, M., 1972, 275 pp. | MR

[11] Babicheva L. A., Bykovtsev G. I., Verveiko N. D., “Luchevoi metod resheniya dinamicheskikh zadach v uprugovyazkoplasticheskikh sredakh”, PMM, 37:1 (1973), 145–155 | Zbl

[12] Bykovtsev G. I., Vlasova I. A., “Luchevoi metod prostranstvennykh zadach teorii idealnoi plastichnosti”, Mekhanika deformiruemogo tverdogo tela, Nauka, Novosibirsk, 1979, 31–36

[13] Burenin A. A., “Ob odnoi vozmozhnosti postroeniya priblizhennykh reshenii nestatsionarnykh zadach dinamiki uprugikh sred pri udarnykh vozdeistviyakh”, Dalnevost. mat. sb., 8 (1999), 49–72

[14] Ivanova Yu. E., Ragozina V. E., “Ob udarnykh osesimmetricheskikh dvizheniyakh neszhimaemoi uprugoi sredy pri udarnykh vozdeistviyakh”, PMTF, 47:6 (2006), 144–151 | Zbl

[15] Ragozina V. E., Voronin I. I., Vekovshinin E. L., “Ob ispolzovanii prifrontovoi asimptotiki v chislennykh resheniyakh dinamicheskikh zadach teorii uprugosti s udarnymi volnami”, Problemy estestvoznaniya i proizvodstva, 115, 1995, 25–27

[16] Burenin A. A., Zinovev P. V., “K probleme vydeleniya poverkhnostei razryvov v chislennykh metodakh dinamiki deformiruemykh sred”, Problemy mekhaniki, Sb. statei k 90-letiyu A. Yu. Ishlinskogo, Fizmatlit, M., 2003, 146–155