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Prox-regularization and solution of ill-posed elliptic variational inequalities

Alexander Kaplan, Rainer Tichatschke (1997)

Applications of Mathematics

In this paper new methods for solving elliptic variational inequalities with weakly coercive operators are considered. The use of the iterative prox-regularization coupled with a successive discretization of the variational inequality by means of a finite element method ensures well-posedness of the auxiliary problems and strong convergence of their approximate solutions to a solution of the original problem. In particular, regularization on the kernel of the differential operator and regularization...

Quantized distributed output regulation of multi-agent systems

Xiaoli Wang, Yumin Chen (2016)

Kybernetika

Motivated by digital communication channel, we consider the distributed output regulation problem for linear multi-agent systems with quantized state measurements. Quantizers take finitely many values and have an adjustable "zoom" parameter. Quantized distributed output regulation concerns designing distributed feedback by employing quantized technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. With the solvability conditions...

Quasi-minima

Mariano Giaquinta, Enrico Giusti (1984)

Annales de l'I.H.P. Analyse non linéaire

Quasi-static evolution for fatigue debonding

Alessandro Ferriero (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The propagation of fractures in a solid undergoing cyclic loadings is known as the fatigue phenomenon. In this paper, we present a time continuous model for fatigue, in the special situation of the debonding of thin layers, coming from a time discretized version recently proposed by Jaubert and Marigo [C. R. Mecanique333 (2005) 550–556]. Under very general assumptions on the surface energy density and on the applied displacement, we discuss the well-posedness of our problem and we give the main...

Quasistatic frictional problems for elastic and viscoelastic materials

Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)

Applications of Mathematics

We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational...

Rate independent Kurzweil processes

Pavel Krejčí, Matthias Liero (2009)

Applications of Mathematics

The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence of solutions in B V spaces. It is shown that in the context of elastoplasticity, the Kurzweil solutions coincide with natural limits of viscous regularizations when the viscosity coefficient tends to zero. The discontinuities produce an additional positive dissipation term, which is not homogeneous of degree...

Regularity results for a class of obstacle problems

Michela Eleuteri (2007)

Applications of Mathematics

We prove some optimal regularity results for minimizers of the integral functional ∫ f ( x , u , D u ) d x belonging to the class K : = { u ∈ W 1 , p ( Ω ) u ≥ ψ } , where ψ is a fixed function, under standard growth conditions of p -type, i.e. L - 1 | z | p ≤ f ( x , s , z ) ≤ L ( 1 + | z | p ) .

Currently displaying 501 – 520 of 669