On certain mathematical models in continuum thermomechanics

被引：13
|
作者：
Zvyagin, V. G. [1 ]
Orlov, V. P. [2 ]
机构：
[1] Voronezh State Univ, Res Inst Math, Voronezh 394006, Russia
[2] Voronezh State Univ, Dept Math, Voronezh 394006, Russia
来源：
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2014年 / 15卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
Thermoviscoelastic continuum; a priori estimates; successive approximations; fixed point theorem; weak solution; weak-renormalized solution; Oberbeck-Boussinesq-type system; objective Jaumann derivative; NONLINEAR PARABOLIC EQUATIONS; NON-NEWTONIAN FLUIDS; PHASE-FIELD MODEL; RENORMALIZED SOLUTIONS; GLOBAL EXISTENCE; COUPLED PROBLEM; WEAK SOLUTIONS; UNIQUENESS; SYSTEM; ENERGY;
D O I：
10.1007/s11784-014-0179-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents results on solvability of multidimensional systems of equations of thermoviscoelasticity. Both compressible and incompressible continua are considered. The existence and uniqueness of regular, weak, and weak-renormalized solutions are given, both local and global. The presented results are based on the successive approximation method combined with an a priori estimates, a fixed point argument and passage to the limit technique. The theory of anisotropic Sobolev spaces with a mixed norm and abstract differential equations are used.
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页码：3 / 47
页数：45
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