A uniqueness theorem for the dynamic initial-displacement boundary value problem in the theory with internal state variables
Author:
Witold Kosiński
Journal:
Quart. Appl. Math. 38 (1980), 129-134
MSC:
Primary 73G99; Secondary 35Q99
DOI:
https://doi.org/10.1090/qam/575836
MathSciNet review:
575836
Full-text PDF Free Access
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Additional Information
- Lewis Wheeler, A uniqueness theorem for the displacement problem in finite elastodynamics, Arch. Rational Mech. Anal. 63 (1976), no. 2, 183–189 (1977). MR 421253, DOI https://doi.org/10.1007/BF00280604
- Lewis Wheeler and R. Ray Nachlinger, On the determinacy of motions for the displacement problem in the dynamics of elastic bodies with viscosity, Z. Angew. Math. Phys. 24 (1973), 601–608 (English, with German summary). MR 339623, DOI https://doi.org/10.1007/BF01588161
W. Kosiński, Uniqueness theorem in the theory of finite inelastic strain, Mech. Res. Comm. 2, 255–260 (1975)
Nguyen Quoc Son, Quasi-static problems for dissipative media (series of lectures at the Summer Course, Jabłonna, May 1978) in Boundary-value problems for dissipative media (in Polish) W. Kosiński (ed.), Ossolineum, Wrocław, 1979
- Oldřich John, On the solution of the displacement boundary-value problem for elastic-inelastic materials, Apl. Mat. 19 (1974), 61–71 (English, with Czech summary). MR 347200
- Jindřich Nečas and Jan Kratochvíl, On the existence of solutions of boundary-value problems for elastic-inelastic solids, Comment. Math. Univ. Carolinae 14 (1973), 755–760. MR 337100
- R. Ray Nachlinger and Jace W. Nunziato, Wave propagation and uniqueness theorems for elastic materials with internal state variables, Internat. J. Engrg. Sci. 14 (1976), no. 1, 31–38. MR 0443513, DOI https://doi.org/10.1016/0020-7225%2876%2990053-7
- P. Perzyna and W. Kosiński, A mathematical theory of materials, Bull. Acad. Polon. Sci. Sér. Sci. Tech. 21 (1973), 1017–1024 (English, with Russian summary). MR 0345499
- W. Kosiński and P. Perzyna, The unique material structures, Bull. Acad. Polon. Sci. Sér. Sci. Tech. 21 (1973), 1025–1032 (English, with Russian summary). MR 0345500
B. D. Coleman and M. E. Gurtin, Thermodynamics with internal state variables, J. Chem. Phys. 47, 597–613 (1967)
K. C. Valanis, Proper tensorial formulation of the internal variable theory, Arch. Mechanics (1)29, 173–185 (1977)
A. Sawczuk (ed.) Foundation of plasticity, problems of plasticity, Noordhoff, Leyden, 1974
- C. Truesdell, Rational thermodynamics, McGraw-Hill Book Co., New York-London-Sydney, 1969. A course of lectures on selected topics; With an appendix on the symmetry of the heat-conduction tensor by C. C. Wang. MR 0366236
L. Wheeler, A uniqueness theorem for the displacement problem in finite elastodynamics, Arch. Ratl. Mech. Anal. 63, 183–189 (1977)
L. Wheeler and R. R. Nachlinger, On the determinacy of motions for the displacement problem in the dynamics of elastic bodies with viscosity, J. Appl. Math. Phys. (ZAMP) (4) 24, 601–608 (1973)
W. Kosiński, Uniqueness theorem in the theory of finite inelastic strain, Mech. Res. Comm. 2, 255–260 (1975)
Nguyen Quoc Son, Quasi-static problems for dissipative media (series of lectures at the Summer Course, Jabłonna, May 1978) in Boundary-value problems for dissipative media (in Polish) W. Kosiński (ed.), Ossolineum, Wrocław, 1979
O. John, On the solution of the displacement boundary-value problem for elastic-inelastic materials, Aplik. Matematiky (2) 19, 61–71 (1974)
J. Nečas and J. Kratochvíl, On the existence of solutions of boundary-value problem for elastic-inelastic solids, Comm. Math. Univ. Car. Praha (4) 14, 755–760 (1973)
R. R. Nachlinger and J. W. Nunziato, Wave propagation and uniqueness theorems for elastic materials with internal state variables, Int. J. Engng Sci. (1) 14, 31–39 (1976)
P. Perzyna and W. Kosiński, A mathematical theory of materials, Bull. Acad. Polon. Sci., Serie Sci. Techn. (12) 21, 647–654 (1973)
W. Kosiński and P. Perzyna, The unique material structures, Bull. Acad. Polon. Sci., Serie Sci. Techn. (12) 21, 655–662 (1973)
B. D. Coleman and M. E. Gurtin, Thermodynamics with internal state variables, J. Chem. Phys. 47, 597–613 (1967)
K. C. Valanis, Proper tensorial formulation of the internal variable theory, Arch. Mechanics (1)29, 173–185 (1977)
A. Sawczuk (ed.) Foundation of plasticity, problems of plasticity, Noordhoff, Leyden, 1974
C. Truesdell, Rational thermodynamics, McGraw-Hill, New York, 1969
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Article copyright:
© Copyright 1980
American Mathematical Society
