A quasistatic frictional contact problem with adhesion for nonlinear elastic materials.
A quasistatic unilateral and frictional contact problem with adhesion for elastic materials
We consider a quasistatic contact problem between a linear elastic body and a foundation. The contact is modelled with the Signorini condition and the associated non-local Coulomb friction law in which the adhesion of the contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation. We derive a variational formulation of the mechanical problem and prove existence of a weak solution if the friction coefficient is sufficiently small....
A quasi-variational inequality problem arising in the modeling of growing sandpiles
Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized...
A regularity result for polyharmonic variational inequalities with thin obstacles
A remark on Gwinner's existence theorem on variational inequality problem.
A remark on polyconvex envelopes of radially symmetric functions in dimension
We study polyconvex envelopes of a class of functions related to the function of Kohn and Strang introduced in . We present an example of a function of this class for which the polyconvex envelope may be computed explicitly and we also point out some general features of the problem.
A remark on quasilinear elliptic variational inequalities with discontinuous coefficients
This Note contains the following remark on a recent result by Boccardo and Buttazzo: under the same assumptions, a stronger conclusion, concerning the solvability of variational inequalities, can be obtained.
A remark on the stability of stationary solutions of parabolic variational inequalities
A self-adaptive method for solving a system of nonlinear variational inequalities.
A stochastic impulse control problem with quadratic growth Hamiltonian and the corresponding quasi variational inequality.
A study of a unilateral and adhesive contact problem with normal compliance
The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation...
A study of variational inequalities for set-valued mappings.
A superquadratic method for solving variational inclusions under weak conditions.
A unilateral boundary-value problem for the rod
A unilateral boundary-value condition at the left end of a simply supported rod is considered. Variational and (equivalent) classical formulations are introduced and all solutions to the classical problem are calculated in an explicit form. Formulas for the energies corresponding to the solutions are also given. The problem is solved and energies of the solutions are compared in the pertubed as well as the unperturbed cases.
A unilateral contact problem with slip-dependent friction
We consider a mathematical model which describes a static contact between a nonlinear elastic body and an obstacle. The contact is modelled with Signorini's conditions, associated with a slip-dependent version of Coulomb's nonlocal friction law. We derive a variational formulation and prove its unique weak solvability. We also study the finite element approximation of the problem and obtain an optimal error estimate under extra regularity for the solution. Finally, we establish the convergence of...
A variational inequality for discontinuous solutions of degenerate parabolic equations.
The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures. The solution is defined via a variational inequality, following Temam?s technique for the evolution problem...
A variational inequality from pricing convertible bond.
A variational model for equilibrium problems in a traffic network
We propose a variational model for one of the most important problems in traffic networks, namely, the network equilibrium flow that is, traditionally in the context of operations research, characterized by minimum cost flow. This model has the peculiarity of being formulated by means of a suitable variational inequality (VI) and its solution is called “equilibrium”. This model becomes a minimum cost model when the cost function is separable or, more general, when the jacobian of the cost operator...
A variational model for equilibrium problems in a traffic network
We propose a variational model for one of the most important problems in traffic networks, namely, the network equilibrium flow that is, traditionally in the context of operations research, characterized by minimum cost flow. This model has the peculiarity of being formulated by means of a suitable variational inequality (VI) and its solution is called “equilibrium”. This model becomes a minimum cost model when the cost function is separable or, more general, when the Jacobian of the cost operator...
A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary