On the well-posedness of the initial value problem for elastic-plastic oscillators with isotropic work-hardening
Author:
Keming Wang
Journal:
Quart. Appl. Math. 53 (1995), 551-558
MSC:
Primary 73E50; Secondary 34A12, 34G20, 47H15, 47N20
DOI:
https://doi.org/10.1090/qam/1343466
MathSciNet review:
MR1343466
Full-text PDF Free Access
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Abstract: The system of differential equations of elastic-plastic oscillators with isotropic work-hardening is converted to a system of differential inclusions and well-posedness is established using maximal monotone operator theory when the external force $f \in {W^{1, 1}}\left ( 0, T; R \right )$. By a more delicate analysis, well-posedness is also established for $f \in {L^1}\left ( 0, T; R \right )$.
J. L. Buhite and D. R. Owen, An ordinary differential equation from the theory of plasticity, Arch. Rational Mech. Anal. 71, 357–383 (1979)
D. R. Owen, Weakly decaying energy separation and uniqueness of motions of an elastic-plastic oscillator with work-hardening, Arch. Rational Mech. Anal. 98, 95–114 (1987)
M. M. Suliciu, I. Suliciu, and W. Williams, On viscoelastic-plastic oscillators, Quart. Appl. Math. 47, 105–116 (1989)
D. R. Owen and K. Wang, Weakly Lipschitzian mappings and restricted uniqueness of solutions of ordinary differential equations, J. Differential Equations 95, 385–398 (1992)
T. Miyoshi, Foundations of the numerical analysis of plasticity, North-Holland, 1985
K. Gröger, Evolution equations in the theory of plasticity, Proc. Fifth Summer School on Nonlinear Operators, Berlin, 1977
K. Gröger, J. Nečas, and L. Trávníček, Dynamic deformation processes of elastic-plastic systems, ZAMM 59, 567–572 (1979)
V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976
E. Zeidler, Nonlinear functional analysis and its applications, Vol. II/A, Springer-Verlag, New York, 1990
H. Brêzis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Studies 5, North Holland, 1973
J. L. Buhite and D. R. Owen, An ordinary differential equation from the theory of plasticity, Arch. Rational Mech. Anal. 71, 357–383 (1979)
D. R. Owen, Weakly decaying energy separation and uniqueness of motions of an elastic-plastic oscillator with work-hardening, Arch. Rational Mech. Anal. 98, 95–114 (1987)
M. M. Suliciu, I. Suliciu, and W. Williams, On viscoelastic-plastic oscillators, Quart. Appl. Math. 47, 105–116 (1989)
D. R. Owen and K. Wang, Weakly Lipschitzian mappings and restricted uniqueness of solutions of ordinary differential equations, J. Differential Equations 95, 385–398 (1992)
T. Miyoshi, Foundations of the numerical analysis of plasticity, North-Holland, 1985
K. Gröger, Evolution equations in the theory of plasticity, Proc. Fifth Summer School on Nonlinear Operators, Berlin, 1977
K. Gröger, J. Nečas, and L. Trávníček, Dynamic deformation processes of elastic-plastic systems, ZAMM 59, 567–572 (1979)
V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, Leyden, 1976
E. Zeidler, Nonlinear functional analysis and its applications, Vol. II/A, Springer-Verlag, New York, 1990
H. Brêzis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Math. Studies 5, North Holland, 1973
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Article copyright:
© Copyright 1995
American Mathematical Society
