Weak solvability of fractional Voigt-alpha model

2021 ◽  
Vol 85 (1) ◽  
Author(s):  
Andrey Viktorovich Zvyagin
Keyword(s):  
Weak Solvability

scholarly journals CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

2010 ◽  
Vol 52 (2) ◽  
pp. 160-178 ◽  
Author(s):  
A. MATEI ◽  
R. CIURCEA
Keyword(s):  
Lagrange Multipliers ◽  
Variational Equation ◽  
Small Deformation ◽  
Contact Problems ◽  
Point Theory ◽  
The Body ◽  
Elastic Materials ◽  
Weak Formulation ◽  
Nonlinearly Elastic ◽  
Weak Solvability

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

scholarly journals Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

2020 ◽  
Vol 25 (6) ◽  
pp. 997-1014
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Difference Scheme ◽  
Numerical Method ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Finite Difference Schemes ◽  
Order Of Accuracy ◽  
Unconditionally Stable ◽  
First Order ◽  
The Difference ◽  
Weak Solvability

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

scholarly journals Singular and Degenerate Boundary Value Problems Related to the Electricity Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Maria-Magdalena Boureanu ◽  
Andaluzia Matei
Keyword(s):  
Sobolev Space ◽  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Weighted Sobolev Space ◽  
Nonlinear Boundary Conditions ◽  
Uniqueness Result ◽  
Physical Phenomena ◽  
Mathematical Literature ◽  
Weak Solvability

The present paper draws attention to the weak solvability of a class of singular and degenerate problems with nonlinear boundary conditions. These problems derive from the electricity theory serving as mathematical models for physical phenomena related to the anisotropic media with “perfect” insulators or “perfect” conductors points. By introducing an appropriate weighted Sobolev space to the mathematical literature, we establish an existence and uniqueness result.

Weak solvability of two quasistatic viscoelastic contact problems

2012 ◽  
Vol 18 (7) ◽  
pp. 745-759 ◽  
Author(s):  
Stanisław Migórski ◽  
Anna Ochal ◽  
Mircea Sofonea
Keyword(s):  
Contact Problems ◽  
Viscoelastic Contact ◽  
Weak Solvability

scholarly journals Weak solvability of fractional Voigt model of viscoelasticity

2018 ◽  
Vol 38 (12) ◽  
pp. 6327-6350 ◽  
Author(s):  
Victor Zvyagin ◽  
◽  
Vladimir Orlov
Keyword(s):  
Voigt Model ◽  
Weak Solvability

scholarly journals Global weak solvability to the regularized viscous compressible heat conductive flow

1991 ◽  
Vol 36 (6) ◽  
pp. 417-431
Author(s):  
Jiří Neustupa ◽  
Antonín Novotný
Keyword(s):  
Weak Solvability
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