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A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Commentationes Mathematicae Universitatis Carolinae

We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result...

A quasistatic contact problem with unilateral constraint and slip-dependent friction

Arezki Touzaline (2015)

Applicationes Mathematicae

We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

Kravvaritis, D., Pantelidis, G. (1996)

Serdica Mathematical Journal

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

A refined Newton’s mesh independence principle for a class of optimal shape design problems

Ioannis Argyros (2006)

Open Mathematics

Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.

A remark on solving large systems of equations in function spaces

I. Bremer, Klaus R. Schneider (1990)

Aplikace matematiky

In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems.

A remark on the local Lipschitz continuity of vector hysteresis operators

Pavel Krejčí (2001)

Applications of Mathematics

It is known that the vector stop operator with a convex closed characteristic Z of class C 1 is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping n is Lipschitz continuous on the boundary ∂ Z of Z . We prove that in the regular case, this condition is also necessary.

A result on segmenting Jungck–Mann iterates

Memudu Olaposi Olatinwo (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, following the concepts in [5, 7], we shall establish a convergence result in a uniformly convex Banach space using the Jungck–Mann iteration process introduced by Singh et al [13] and a certain general contractive condition. The authors of [13] established various stability results for a pair of nonself-mappings for both Jungck and Jungck–Mann iteration processes. Our result is a generalization and extension of that of [7] and its corollaries. It is also an improvement on the result...

A simple regularization method for the ill-posed evolution equation

Nguyen Huy Tuan, Dang Duc Trong (2011)

Czechoslovak Mathematical Journal

The nonhomogeneous backward Cauchy problem u t + A u ( t ) = f ( t ) , u ( T ) = ϕ , where A is a positive self-adjoint unbounded operator which has continuous spectrum and f is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.

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