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Existence theory for the equations of inelastic material behaviour of metals - Transformation of interior variables and energy estimates

Chelminski, Krzysztof ; Alber, Hans-Dieter (1996):
Existence theory for the equations of inelastic material behaviour of metals - Transformation of interior variables and energy estimates.
In: Roczniki Polskiego Towarzystwa Matematycznego Seria 3, 25 (39), pp. 3-15. Polish Mathematical Society, ISSN 0137-2890,
DOI: 10.14708/ma.v25i39.1844,
[Article]

Abstract

The system of equations, which we study, consists of linear partial differential equations and of nonlinear ordinary differential equations for internal variables. The existence theory for such systems was studied first by the french mathematicians G. Duvaut and J.L. Lions [1]. Next we can find in the literature a work of C. Johnson [2] on a quasi-static problem for a special model. Then in the nineties we can find more works in the domain. This work consists of two parts. In the first part we will classify constitutive equations and therefore we define constitutive equations of monotone type. Moreover by transformation of internal variables we will enlarge the class of constitutive equations, for which we can prove a. global in time existence theorem for large initial data. But there exist models, which are not of monotone type and which we can not transform to monotone type. Therefore we must study such models with other methods. This is the second part, of the work. We write about the energy method for the model of Bodner-Partom.

Item Type: Article
Erschienen: 1996
Creators: Chelminski, Krzysztof ; Alber, Hans-Dieter
Title: Existence theory for the equations of inelastic material behaviour of metals - Transformation of interior variables and energy estimates
Language: English
Abstract:

The system of equations, which we study, consists of linear partial differential equations and of nonlinear ordinary differential equations for internal variables. The existence theory for such systems was studied first by the french mathematicians G. Duvaut and J.L. Lions [1]. Next we can find in the literature a work of C. Johnson [2] on a quasi-static problem for a special model. Then in the nineties we can find more works in the domain. This work consists of two parts. In the first part we will classify constitutive equations and therefore we define constitutive equations of monotone type. Moreover by transformation of internal variables we will enlarge the class of constitutive equations, for which we can prove a. global in time existence theorem for large initial data. But there exist models, which are not of monotone type and which we can not transform to monotone type. Therefore we must study such models with other methods. This is the second part, of the work. We write about the energy method for the model of Bodner-Partom.

Journal or Publication Title: Roczniki Polskiego Towarzystwa Matematycznego Seria 3
Journal Volume: 25
Issue Number: 39
Publisher: Polish Mathematical Society
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Analysis
Date Deposited: 19 Nov 2008 16:02
DOI: 10.14708/ma.v25i39.1844
Additional Information:

ab 2000: Matematyka Stosowana-Applied Mathematics (ISSN 1730-2668)

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