Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
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Avtandil Gachechiladze
Abstract
We study three-dimensional unilateral contact problems with friction for hemitropic elastic solids. We give their mathematical formulation in the form of spatial variational inequalities and show the equivalence to the corresponding minimization problem. Based on our variational inequality approach, we prove existence and uniqueness theorems. We prove also that solutions continuously depend on the data of the original problem and on the friction coefficient. Our investigation includes the special particular case of only traction-contact boundary conditions without prescribing displacement and microrotation vectors along some part of the boundary of a hemitropic elastic body. Then the problems are not unconditionally solvable and we derive the necessary and sufficient conditions of their solvability.
© Heldermann Verlag
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Articles in the same Issue
- On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
- Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
- Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
- A Periodic Boundary Value Problem for Functional Differential Equations of Higher Order
- The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
- Stability by Fixed Point Theory for Nonlinear Delay Difference Equations
- On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant
- On Nonmeasurable Functions of Two Variables and Iterated Integrals
- Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems
- On Functional Equations Connected with Quadrature Rules
- The Riemann–Hilbert Problem in a Domain with Piecewise Smooth Boundaries in Weight Classes of Cauchy Type Integrals with a Density from Variable Exponent Lebesgue Spaces
- A Counterexample on Embedding of Spaces
- On Solutions of a Singular Viscoelastic Equation with an Integral Condition
- Nonbounding 𝑛-C.E. 𝑄-Degrees
- Nonequivalence of Unilateral Strong Differentiation Bases in
