Weak Solvability of Frictional Problems for Piezoelectric Bodies in Contact with a Conductive Foundation

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.

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

Nonlinear Analysis Modelling and Control ◽

10.15388/namc.2020.25.20558 ◽

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.

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Weak Solvability of One Viscoelastic Fractional Dynamics Model of Continuum with Memory

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-020-00525-3 ◽

2020 ◽

Vol 23 (1) ◽

Author(s):

V. G. Zvyagin ◽

V. P. Orlov

Keyword(s):

Fractional Dynamics ◽

Dynamics Model ◽

With Memory ◽

Weak Solvability

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Weak solvability of fractional Voigt-alpha model

Izvestiya Mathematics ◽

10.1070/im9020 ◽

2021 ◽

Vol 85 (1) ◽

Author(s):

Andrey Viktorovich Zvyagin

Keyword(s):

Weak Solvability

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On the Weak Solvability Via Lagrange Multipliers for a Bingham Model

Mediterranean Journal of Mathematics ◽

10.1007/s00009-020-01596-2 ◽

2020 ◽

Vol 17 (5) ◽

Author(s):

Mariana Chivu Cojocaru ◽

Andaluzia Matei

Keyword(s):

Lagrange Multipliers ◽

Bingham Model ◽

Weak Solvability

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Singular and Degenerate Boundary Value Problems Related to the Electricity Theory

Mathematical Problems in Engineering ◽

10.1155/2015/865261 ◽

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.

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