Geodesic
A mathematical model of the motion of shear shock waves of nonzero curvature based on their evolution equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 77-85.

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We study particular features of the appearance and motion of 1-dimensional shear shock waves of nonzero curvature basing on the corresponding evolution equation. Using numerous examples of boundary value problems for axisymmetric antiplane deformation, we demonstrate the efficiency of applying solutions to the evolution equation as the frontal asymptotics in the method of matched asymptotic expansions.
Keywords: nonlinear elasticity, incompressibility, shock wave
Mots-clés : perturbation method, evolution equation. 
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V. E. Ragozina; Yu. E. Ivanova. A mathematical model of the motion of shear shock waves of nonzero curvature based on their evolution equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 77-85. http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a7/

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

[2] Burenin A. A., Chernyshov A. D., “Udarnye volny v izotropnom uprugom prostranstve”, Prikl. matematika i mekhanika, 42:4 (1978), 711–717

[3] Blend D., Nelineinaya dinamicheskaya teoriya uprugosti, Mir, M., 1972

[4] Koul Dzh., Metody vozmuschenii v prikladnoi matematike, Mir, M., 1972

[5] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977

[6] 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 | Zbl

[7] Ivanova Yu. E., Ragozina V. E., “Ob udarnykh osesimmetricheskikh dvizheniyakh neszhimaemoi uprugoi sredy pri udarnykh vozdeistviyakh”, Prikl. mekhanika i i tekhn. fizika, 47:6 (2006), 144–151 | Zbl

[8] Burenin A. A., Ragozina V. E., Ivanova Yu. E., “Evolyutsionnoe uravnenie dlya volnovykh protsessov formoizmeneniya”, Izvestiya SGU. Ser. Matematika. Mekhanika. Informatika, 9:4, ch. 2 (2009), 14–24

[9] Pelinovskii Yu. N., Fridman V. E., Engelbrekht Yu. K., Nelineinye evolyutsionnye uravneniya, Valgus, Tallinn, 1984

[10] Ragozina V. E., Ivanova Yu. E., “Ob evolyutsionnykh uravneniyakh zadach udarnogo deformirovaniya s ploskimi poverkhnostyami razryvov”, Vychisl. mekhanika sploshnykh sred, 2:3 (2009), 82–95

[11] Bykovtsev G. I., Ivlev D. D., Teoriya plastichnosti, Dalnauka, Vladivostok, 1998

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

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

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

[15] 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, M., 2003, 146–155