Conservation laws in nonlinear elasticity. I. One-dimensional elastodynamics
Author:
L. G. Vulkov
Journal:
Quart. Appl. Math. 52 (1994), 427-438
MSC:
Primary 73C50; Secondary 35L65, 73D99
DOI:
https://doi.org/10.1090/qam/1292195
MathSciNet review:
MR1292195
Full-text PDF Free Access
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Additional Information
C. Atkinson, Stress singularities and fracture mechanics, Appl. Mech. Rev. 32, 123–135 (1979)
J. Rice, A path-independent integral and approximate analysis of strain concentration by notches and cracks, J. Appl. Mech. 35, 379–386 (1968)
P. J. Olver, Conservation laws in elasticity. I, Arch. Rational. Mech. Anal. 85, 131–160 (1984)
J. K. Knowles and E. Sternberg, On a class of conservation laws in linear and finite elasto-statics, Arch. Rational. Mech. Anal. 44, 187–211 (1972)
D. C. Fletcher, Conservation laws in linear elastodynamics, Arch. Rational. Mech. Anal. 60, 329–353 (1976)
J. Qing, Conservation laws in linear visco-elastodynamics, J. of Elasticity 16, 213–219 (1986)
L. U. Ovsiannǐkov, Group Analysis of Equations, Academic Press, New York, 1982
P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986
J. M. Ball, Convexity conditions and existence theorems in non-linear elasticity, Arch. Rational. Mech. Anal. 63, 337–403 (1977)
D. Terentev and J. D. Smyglevski, Full set divergent equations of ideal gas dynamics, Zh. Vychisl. Mat. i Mat. Fiz. 15 1535–1544 (1976) (in Russian)
L. G. Vulkov, On the conservation laws in magnetohydrodynamics in infini co conductivity, Zh. Vychisl. Mat. i Mat. Fiz. 25, 1401–1408 (1985) (in Russian)
C. A. Truesdell and W. Noll, The Non-linear Field Theories of Mechanics, in Handbuch der Physik, S. Fugge (Ed.), vol. III/3, Springer, Berlin (1965)
B. L. Rozdestvenskii and N. N. Janenko, Systems of Quasilinear Equations, Nauka, Moscow, 1968 (in Russian)
C. Dafermos, The equations of elasticity are special, Trends and Appl. of Pure Math. in Mech. V, 96–103 (1981)
W. D. Collins, One-dimensional non-linear wave propagation in incompressible elastic materials, Quart. J. Mech. Appl. Math. XIX, Pt. 3, 259–328 (1965)
C. Atkinson, Stress singularities and fracture mechanics, Appl. Mech. Rev. 32, 123–135 (1979)
J. Rice, A path-independent integral and approximate analysis of strain concentration by notches and cracks, J. Appl. Mech. 35, 379–386 (1968)
P. J. Olver, Conservation laws in elasticity. I, Arch. Rational. Mech. Anal. 85, 131–160 (1984)
J. K. Knowles and E. Sternberg, On a class of conservation laws in linear and finite elasto-statics, Arch. Rational. Mech. Anal. 44, 187–211 (1972)
D. C. Fletcher, Conservation laws in linear elastodynamics, Arch. Rational. Mech. Anal. 60, 329–353 (1976)
J. Qing, Conservation laws in linear visco-elastodynamics, J. of Elasticity 16, 213–219 (1986)
L. U. Ovsiannǐkov, Group Analysis of Equations, Academic Press, New York, 1982
P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986
J. M. Ball, Convexity conditions and existence theorems in non-linear elasticity, Arch. Rational. Mech. Anal. 63, 337–403 (1977)
D. Terentev and J. D. Smyglevski, Full set divergent equations of ideal gas dynamics, Zh. Vychisl. Mat. i Mat. Fiz. 15 1535–1544 (1976) (in Russian)
L. G. Vulkov, On the conservation laws in magnetohydrodynamics in infini co conductivity, Zh. Vychisl. Mat. i Mat. Fiz. 25, 1401–1408 (1985) (in Russian)
C. A. Truesdell and W. Noll, The Non-linear Field Theories of Mechanics, in Handbuch der Physik, S. Fugge (Ed.), vol. III/3, Springer, Berlin (1965)
B. L. Rozdestvenskii and N. N. Janenko, Systems of Quasilinear Equations, Nauka, Moscow, 1968 (in Russian)
C. Dafermos, The equations of elasticity are special, Trends and Appl. of Pure Math. in Mech. V, 96–103 (1981)
W. D. Collins, One-dimensional non-linear wave propagation in incompressible elastic materials, Quart. J. Mech. Appl. Math. XIX, Pt. 3, 259–328 (1965)
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Article copyright:
© Copyright 1994
American Mathematical Society
