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

## 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 1996 Chelminski, Krzysztof ; Alber, Hans-Dieter Bibliographie Existence theory for the equations of inelastic material behaviour of metals - Transformation of interior variables and energy estimates English 1996 Polish Mathematical Society Roczniki Polskiego Towarzystwa Matematycznego Seria 3 25 39 10.14708/ma.v25i39.1844 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. ab 2000: Matematyka Stosowana-Applied Mathematics (ISSN 1730-2668) 04 Department of Mathematics04 Department of Mathematics > Analysis 19 Nov 2008 16:02 03 May 2022 07:48 IBW_RDADublin CoreRDF+XMLASCII CitationHTML CitationEP3 XMLMultiline CSVT2T_XMLAtomJSONBibTeXMODSEndNoteSimple Metadata TUfind oder in Google
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