The axisymmetric Boussinesq-type problem for a half-space under optimal heating of arbitrary profile.
The basic mixed problem for an anisotropic elastic body.
The boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of the boundaries.
The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input state” map in -norms is established. A structure of the reachable sets for arbitrary is studied. In general case, only the first component of the complete state may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....
The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation
The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input → state" map in L2-norms is established. A structure of the reachable sets for arbitrary T>0 is studied. In general case, only the first component of the complete state may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....
The energy method for elastic problems with non-homogeneous boundary conditions
In this paper we propose the weighted energy method as a way to study estimates of solutions of boundary-value problems with non-homogeneous boundary conditions in elasticity. First, we use this method to study spatial decay estimates in two-dimensional elasticity when we consider non-homogeneous boundary conditions on the boundary. Some comments in the case of harmonic vibrations are considered as well. We also extend the arguments to a class of three-dimensional problems in a cylinder. A section...
The version of the finite element method with quasiuniform meshes
The interface crack with Coulomb friction between two bonded dissimilar elastic media
We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.
The Korn inequality for Jones domains.
The second fundamental coupled problem of the theory of thermoelasticity for an infinite strip.
The shape of the free surface of a unilaterally supported elastic body
The spectrum of the elasticity problem for a spiked body.
The three-dimensional problem of statics of the elastic mixture theory with displacements given on the boundary.
Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition
This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Durán et al. (cf. [Numer. Math.107 (2007) 295–314; IMA J. Appl. Math.71 (2006) 853–876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important...
Thermoelastic equilibrium of bodies in generalized cylindrical coordinates.
Two-dimensional problems of elasticity of anisotropic bodies.