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.

引用

页码：3 / 47

页数：45

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