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

Hans-Dietmer Alber, and Krzysztof Chełmiński. "Existence theory for the equations of inelastic material behavior of metals - Transformation of interior variables and energy estimates." Mathematica Applicanda 25.39 (1996): null. <http://eudml.org/doc/292850>.

@article{Hans1996,
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.},
author = {Hans-Dietmer Alber, Krzysztof Chełmiński},
journal = {Mathematica Applicanda},
keywords = {Time-dependent problems; Equations of mathematical physics and other areas of application},
language = {eng},
number = {39},
pages = {null},
title = {Existence theory for the equations of inelastic material behavior of metals - Transformation of interior variables and energy estimates},
url = {http://eudml.org/doc/292850},
volume = {25},
year = {1996},
}

TY - JOUR
AU - Hans-Dietmer Alber
AU - Krzysztof Chełmiński
TI - Existence theory for the equations of inelastic material behavior of metals - Transformation of interior variables and energy estimates
JO - Mathematica Applicanda
PY - 1996
VL - 25
IS - 39
SP - null
AB - 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.
LA - eng
KW - Time-dependent problems; Equations of mathematical physics and other areas of application
UR - http://eudml.org/doc/292850
ER -