On parabolic quasi-variational inequalities and state-dependent sweeping processes

Kunze, Markus; Marques, Manuel

doi:10.12775/tmna.1998.036

Cited by 55 publications

(38 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It has been introduced and studied for the first time for convex sets C(t, x) in R 3 by Chraibi Kaadoud [10] in view of modeling of some mechanical problems. Later, Kunze and Monteiro Marques [21] proved the existence of solution for convex sets C(t, x) in R n (see also [11]) and they also studied the case of Hilbert space under some compactness condition. Because of the presence of the normal cone, for any solution u(·), we see that u(t) is constrained to stay in C (t, u(t)).…”

Section: Introductionmentioning

confidence: 99%

“…On the contrary, the existence of solutions for (1.1) and (1.2) in infinite dimensions (without any compactness-type assumption) is still an open problem. In addition to friction mechanical problems, we mention that the interest in the study of the state dependent sweeping processes (1.1) and (1.2) arises in connection with the treatment of quasistatical evolution problems, micromechanical damage models (see [10,11,21,22] and the references therein), and the evolution of shape memory alloys [1,2].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reduction of state dependent sweeping process to unconstrained differential inclusion

2014

View full text Add to dashboard Cite

In this article we discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets. We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state dependent sweeping process with unbounded perturbations. The perturbations are not required to be convex valued.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reduction of state dependent sweeping process to unconstrained differential inclusion

2014

View full text Add to dashboard Cite

show abstract

“…Very recently our attention has been drawn to a preprint of December 1997 by Kunze (University of Köln) and Monteiro Marques (University of Lisbon) entitled "On parabolic quasi-variational inequalities and state-dependent sweeping process" where a result similar to Theorem 2.1 has been proved by a different method. This paper has now appeared [7]. In a recent paper of Lions [8], it is observed in Remark 6.3 that one can extend the methods of the present paper to some quasivariational inequalities.…”

Section: Evolution Quasi-variational Inequalities Ofmentioning

confidence: 62%

Certain remarks on a class of evolution quasi‐variational inequalities

Siddiqi

Manchanda

2000

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

Abstract. We prove two existence theorems, one for evolution quasi-variational inequalities and the other for a time-dependent quasi-variational inequality modeling the quasistatic problem of elastoplasticity with combined kinetic-isotropic hardening.Keywords and phrases. Evolution quasi-variational inequalities, coercive, weakly convergent, weakly continuous, weak topology. [12] have studied numerical solutions of quasivariational inequalities using techniques of nonsmooth optimization. The evolution quasi-variational inequality modeling the evolving shape of a growing pile has been studied by Prigozhin [13]. Han, Reddy, and Schroeder [5] have investigated a new class of evolution inequalities where rate quantities occur in all of its terms. An inequality of this type represents, for example, the quasi-static evolution of an elastoplastic body where the stress law is of the linear kinematic or isotropic hardening type. Such a variational inequality may be useful in the modeling of financial derivatives and option pricing, see Wilmott et al. [14]. In this paper, we discuss the existence of solutions of the implicit evolution quasi-variational inequalities. In Section 2, we present an existence theorem which is closely related to an open problem mentioned in [13]. The evolution quasi-variational inequality problem of the Han-Reddy-Schroeder type is considered in Section 3.

show abstract

“…Thus {z α } ≡ z α is continuous on [0, η 0 ]. From the chain of integrators in (34) we see also that the functions {z k } ≡ z k are continuous on…”

Section: Proofmentioning

confidence: 99%

Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

2006

View full text Add to dashboard Cite

In this paper we present an extension of Moreau's sweeping process for higher order systems. The dynamical framework is carefully introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization of these nonsmooth systems with a timestepping algorithm is also presented. This differential inclusion can be seen as a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementaryslackness variables. Applications of such high-order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes.

show abstract

On parabolic quasi-variational inequalities and state-dependent sweeping processes

Cited by 55 publications

References 2 publications

Reduction of state dependent sweeping process to unconstrained differential inclusion

Reduction of state dependent sweeping process to unconstrained differential inclusion

Certain remarks on a class of evolution quasi‐variational inequalities

Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

Contact Info

Product

Resources

About