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Summary:
The system of equations which describe the model with the so-called internal state variables in continuum mechanics is studied. A theorem asserting the existence and uniqueness of a solution of the displacement boundary-value problem is proved by combining the theory of monotone operators and the Banach contraction principle.
References:
[1] J. Kratochvíl O. W. Dillon: Thermodynamics of Elastic-Plastic Materials as a Theory with Internal State Variables. Journal of Applied Physics, Vol. 40, No. 8, 3207-3218, 1969.
[2] J. Kratochvíl O. W. Dillon: Thermodynamics of Crystalline Elastic-Visco-Plastic Materials. Journal of Applied Physics, Vol. 41, No. 4, 1470-1479, 1970. DOI 10.1063/1.1659058
[3] J. Kratochvíl J. Nečas: On the Solution of the Traction Boundary Vaiue Problem for Elastic-Inelastic Materials. CMUC 14 (4), 1973, 755-760. MR 0337100
[4] I. Hlaváček J. Nečas: On Inequalities of Korn's Type. Part I, II. Archive for Rational Mechanics and Analysis, Vol. 36, No. 4, 1970.
[5] S. Fučík J. Nečas V. Souček: Introduction to the Variational Calculus. (Czech.) Lecture Notes of Prague University, 1972.
[6] Вайнберг M. M.: Вариационный метод и метод монотонных операторов. Наука, Москва 1972. Zbl 1156.34335
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