Divergence measure fields and Cauchy’s stress theorem
Rendiconti del Seminario Matematico della Università di Padova (2005)
- Volume: 113, page 15-45
- ISSN: 0041-8994
Access Full Article
topHow to cite
topSilhavy, Miroslav. "Divergence measure fields and Cauchy’s stress theorem." Rendiconti del Seminario Matematico della Università di Padova 113 (2005): 15-45. <http://eudml.org/doc/108654>.
@article{Silhavy2005,
author = {Silhavy, Miroslav},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {15-45},
publisher = {Seminario Matematico of the University of Padua},
title = {Divergence measure fields and Cauchy’s stress theorem},
url = {http://eudml.org/doc/108654},
volume = {113},
year = {2005},
}
TY - JOUR
AU - Silhavy, Miroslav
TI - Divergence measure fields and Cauchy’s stress theorem
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2005
PB - Seminario Matematico of the University of Padua
VL - 113
SP - 15
EP - 45
LA - eng
UR - http://eudml.org/doc/108654
ER -
References
top- [1] S. S. ANTMAN - J. E. OSBORN, The principle of virtual work and integral laws of motion, Arch. Rational Mech. Anal., 69 (1979), pp. 231-262. Zbl0403.73003MR522525
- [2] G. ANZELLOTTI, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl., 135 (1983), pp. 293-318. Zbl0572.46023MR750538
- [3] C. BANFI - M. FABRIZIO, Sul concetto di sottocorpo nella meccanica dei continui, Rend. Acc. Naz. Lincei, 66 (1979), pp. 136-142. Zbl0446.73006MR606078
- [4] G.-Q. CHEN - H. FRID, On the Theory of Divergence-Measure Fields and Its Applications, Boletim da Sociedade Brasileira de Matemática (Bol. Soc. Bras. Math.), 32 (2001), pp. 1-33. Zbl1024.28009MR1894566
- [5] G.-Q. CHEN - H. FRID, Extended Divergence-Measure Fields and the Euler Equations for Gas Dynamics, Communications in Mathematical Physics, 236 (2003), pp. 251-280. Zbl1036.35125MR1981992
- [6] G.-Q. CHEN - H. FRID, Divergence-Measure Fields and Hyperbolic Conservation Laws, Arch. Rational Mech. Anal., 147 (1999), pp. 89-118. Zbl0942.35111MR1702637
- [7] M. DEGIOVANNI - A. MARZOCCHI - A. MUSESTI, Cauchy fluxes associated with tensor fields having divergence measure, Arch. Rational Mech. Anal., 147 (1999), pp. 197-223. Zbl0933.74007MR1709215
- [8] N. DUNFORD - J. T. SCHWARTZ, Linear Operators: Part I: General Theory, New York, Willey (1958). Zbl0084.10402MR1009162
- [9] K. FALCONER, Fractal geometry, Chichester, Willey (1990). Zbl0689.28003MR1102677
- [10] H. FEDERER, Geometric measure theory, New York, Springer (1969). Zbl0176.00801MR257325
- [11] R. FOSDICK - E. VIRGA, A variational proof of the stress theorem of Cauchy, Arch. Rational Mech. Anal., 105 (1989), pp. 95-103. Zbl0658.73002MR968456
- [12] R. V. KOHN - R. TEMAM, Dual spaces of stresses and strains, Appl. Math. Optimization, 10 (1983), pp. 1-35. Zbl0532.73039MR701898
- [13] M. E. GURTIN - L. C. MARTINS, Cauchy's theorem in classical physics, Arch. Rational Mech. Anal., 60 (1976), pp. 305-324. Zbl0347.73001MR408377
- [14] M. E. GURTIN - W. O. WILLIAMS - W. ZIEMER, Geometric measure theory and the axioms of continuum mechanics, Arch. Rational Mech. Anal., 92 (1985), pp. 1-22. Zbl0599.73002MR816619
- [15] A. MARZOCCHI - A. MUSESTI, Decomposition and integral representation of Cauchy interactions associated with measures, Continuum Mech. Thermodyn., 13 (2001), pp. 149-169. Zbl1019.74003MR1857126
- [16] A. MARZOCCHI - A. MUSESTI, On the measure-theoretic foundations of the second law of thermodynamics, Math. Models Methods Appl. Sci., 12 (2002), pp. 721-736. Zbl1205.80003MR1909424
- [17] A. MARZOCCHI - A. MUSESTI, Balanced powers in continuum mechanics, Meccanica, 38 (2003), pp. 369-389. Zbl1062.74003MR1981023
- [18] A. MARZOCCHI - A. MUSESTI, The Cauchy stress theorem for bodies with finite perimeter, Rend. Sem. Mat. Univ. Padova, 109 (2003), pp. 1-11. Zbl1165.74300MR1997983
- [19] W. NOLL, The foundations of classical mechanics in the light of recent advances in continuum mechanics, in The Axiomatic Method, with Special Reference to Geometry and Physics, P. Suppes (ed). North-Holland, Amsterdam 1959 pp. 266-281. Zbl0087.39401MR108036
- [20] W. NOLL - E. G. VIRGA, Fit regions and functions of bounded variation, Arch. Rational Mech. Anal., 102 (1988), pp. 1-21. Zbl0668.73005MR938381
- [21] G. RODNAY - R. SEGEV, Cauchy's flux theorem in light of the geometric integration theory, J. Elasticity, 71 (2002), pp. 183-203 Preprint, 2002. Zbl1156.74305MR2042680
- [22] C. A. ROGERS, Hausdorff measures, Cambridge, Cambridge University Press (1970). Zbl0204.37601MR281862
- [23] R. SEGEV, The geometry of Cauchy's fluxes, Arch. Rational Mech. Anal., 154 (2000), pp. 183-198. Zbl0965.58004MR1785472
- [24] M. SÏILHAVÝ, The existence of the flux vector and the divergence theorem for general Cauchy fluxes, Arch. Rational Mech. Anal., 90 (1985), pp. 195-212. Zbl0593.73007MR803773
- [25] M. SÏILHAVý, Cauchy's stress theorem and tensor fields with divergences in Lp , Arch. Rational Mech. Anal., 116 (1991), pp. 223-255. Zbl0776.73003MR1132761
- [26] R. TEMAM, Navier-Stokes equations, Amsterdam, North-Holland (1977). Zbl0383.35057MR603444
- [27] R. L. WHEEDEN - S. ZYGMUND, Measure and integral, New York and Basel, M. Dekker (1977). Zbl0362.26004MR492146
- [28] H. WHITNEY, Geometric integration theory, Princeton, Princeton University Press (1957). Zbl0083.28204MR87148
- [29] W. ZIEMER, Cauchy flux and sets of finite perimeter, Arch. Rational Mech. Anal., 84 (1983), pp. 189-201. Zbl0531.73005MR714974
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.