Dynamical contact problems with friction for hemitropic elastic solids
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Abstract.
In the present paper we investigate a three-dimensional boundary-contact problem of dynamics for a homogeneous hemitropic elastic medium with regard to friction. We prove the uniqueness theorem using the corresponding Green formulas and positive definiteness of the potential energy. To analyze the existence of solutions we reduce equivalently the problem under consideration to a spatial variational inequality. We consider a special parameter-dependent regularization of this variational inequality which is equivalent to the relevant regularized variational equation depending on a real parameter and study its solvability by the Faedo–Galerkin method. Some a priori estimates for solutions of the regularized variational equation are established and with the help of an appropriate limiting procedure the existence theorem for the original contact problem with friction is proved.
© 2014 by Walter de Gruyter Berlin/Boston
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- Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces
- q-Dunkl-classical q-Hermite type polynomials
- Spectral representation of a Banach-valued stationary random function on a locally compact abelian group
- Sharp weighted norm inequalities for the commutator of Littlewood–Paley operators
- On rearrangement theorems in Banach spaces
- Dynamical contact problems with friction for hemitropic elastic solids
- Multiple solutions for a Dirichlet quasilinear system containing a parameter
- Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝN+1
- A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities
- Transformation of the quasiconformal reflection coefficient and of the Fredholm eigenvalue
- Expansions and asymptotics associated with basic hypergeometric functions and modified q-Bessel functions
Articles in the same Issue
- Frontmatter
- Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces
- q-Dunkl-classical q-Hermite type polynomials
- Spectral representation of a Banach-valued stationary random function on a locally compact abelian group
- Sharp weighted norm inequalities for the commutator of Littlewood–Paley operators
- On rearrangement theorems in Banach spaces
- Dynamical contact problems with friction for hemitropic elastic solids
- Multiple solutions for a Dirichlet quasilinear system containing a parameter
- Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝN+1
- A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities
- Transformation of the quasiconformal reflection coefficient and of the Fredholm eigenvalue
- Expansions and asymptotics associated with basic hypergeometric functions and modified q-Bessel functions
