@article{VNGU_2016_16_3_a4,
author = {A. O. Molchanova},
title = {A variational approximation scheme for the elastodynamic problems in the new class of admissible mappings},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {55--60},
year = {2016},
volume = {16},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a4/}
}
TY - JOUR AU - A. O. Molchanova TI - A variational approximation scheme for the elastodynamic problems in the new class of admissible mappings JO - Sibirskij žurnal čistoj i prikladnoj matematiki PY - 2016 SP - 55 EP - 60 VL - 16 IS - 3 UR - http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a4/ LA - ru ID - VNGU_2016_16_3_a4 ER -
%0 Journal Article %A A. O. Molchanova %T A variational approximation scheme for the elastodynamic problems in the new class of admissible mappings %J Sibirskij žurnal čistoj i prikladnoj matematiki %D 2016 %P 55-60 %V 16 %N 3 %U http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a4/ %G ru %F VNGU_2016_16_3_a4
A. O. Molchanova. A variational approximation scheme for the elastodynamic problems in the new class of admissible mappings. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 16 (2016) no. 3, pp. 55-60. http://geodesic.mathdoc.fr/item/VNGU_2016_16_3_a4/
[1] Ball J. M., “Convexity Conditions and Existence Theorems in Nonlinear Elasticity”, Arch. Ration. Mech. Anal., 63 (1977), 337–403 | DOI
[2] Ball J. M., “Some Open Problems in Elasticity”, Geometry, Mechanics, and Dynamics, eds. P. Newton et al., Springer, N.Y., 2002, 3–59 | DOI
[3] P. G. Ciarlet, Mathematical Elasticity, v. 1, North Holland, Amsterdam, 1993
[4] Dafermos C. M., Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, Berlin–Heidelberg, 2010
[5] Di Perna R., “Convergence of Approximate Solutions to Conservation Laws”, Arch. Ration. Mech. Anal., 82 (1983), 27–70 | DOI
[6] Demoulini S., Stuart D. M. A., Tzavaras A. E., “A Variational Approximation Scheme for Three Dimensional Elastodynamics with Polyconvex Energy”, Arch. Ration. Mech. Anal., 157 (2001), 324–344 | DOI
[7] De Giorgi E., “New Problems on Minimizing Movements”, Boundary Value Problems for PDEs and Applications, Res. Notes in Appl. Math., 29, 1993, 81–98
[8] Qin T., “Symmetrizing Nonlinear Elasodynamics System”, J. Elasticity, 50 (1998), 245–252 | DOI
[9] Iwaniec T., Šverák V., “On Mappings with Integrable Dilatation”, Proc. Amer. Math. Soc., 118 (1993), 185–188 | DOI
[10] Miroshnikov A., Tzavaras A., “A Variational Approximation Scheme for Radial Polyconvex Elasticity That Preserves the Positivity of Jacobians”, Comm. Math. Sciences, 10:1 (2012), 87–115 | DOI
[11] Molchanova A. O., Vodop'yanov S. K., Variational Problems of Nonlinear Elasticity Theory in Certain Classes of Mappings with Finite Distortion, arXiv: 1508.06825v1
[12] S. K. Vodop'yanov, A. O. Molchanova, “Variational problems of nonlinear elasticity theory in certain classes of mappings with finite distortion”, Dokl. Math., 92:3 (2015), 739–742 | DOI | DOI