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Évolution quasi-statique des milieux visco-plastiques de Maxwell- Norton. (French) Zbl 0563.73024
The authors consider the quasistatic problem for a viscoplastic body described by a Maxwell-Norton constitutive equation which allows to define a convex potential of forces. Some basical results concerning the functional space of the problem are recalled. When some condition for the initial and boundary data are fullfilled the problem may be reduced to a homogeneous one. In order to solve this problem an implicit scheme in time is performed. Some a priori estimates of solutions are given which are employed together with some monotonicity techniques in order to prove the convergence of the discrete solution to the solution of the initial problem.
Reviewer: V.Tigoiu

74C99 Plastic materials, materials of stress-rate and internal-variable type
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35G99 General higher-order partial differential equations and systems of higher-order partial differential equations
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[1] Friaa, Le matériau de Norton-Hoff généralisé et ses applications en analyse limite, C. R. Acad. Sci. Paris 286 pp 953– (1978)
[2] Geymonat , G. Suquet , P. Espaces fonctionnels pour les milieux de Norton-Hoff
[3] Pelissier , M. C. Sur quelques problèmes non linéaires en glaciologie 1975
[4] Lions , J. L. Problèmes aux limites dans les équations aux dérivées partielles 1962
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