Set-valued perturbation to second-order evolution problems with time-dependent subdifferential operators

2021 ◽  
Author(s):  
Soumia Saïdi
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Separable Hilbert Space ◽  
Existence Of Solutions ◽  
Second Order ◽  
Time Dependent ◽  
Evolution Inclusion ◽  
Evolution Problems ◽  
Quasi Variational Inequality ◽  
Subdifferential Operators

The main purpose of this work is to study the existence of solutions for a perturbed second-order evolution inclusion involving time-dependent subdifferential operators. Under suitable conditions on the set-valued perturbation, the main result of the paper is proved in the context of a separable Hilbert space. A second-order evolution quasi-variational inequality is also investigated.

scholarly journals Certain remarks on a class of evolution quasi-variational inequalities

2000 ◽  
Vol 24 (12) ◽  
pp. 851-855 ◽  
Author(s):  
A. H. Siddiqi ◽  
Pammy Manchanda
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Existence Theorems ◽  
Static Problem ◽  
The Other ◽  
Time Dependent ◽  
Isotropic Hardening ◽  
Quasi Variational Inequality

We prove two existence theorems, one for evolution quasi-variational inequalities and the other for a time-dependent quasi-variational inequality modeling the quasi-static problem of elastoplasticity with combined kinetic-isotropic hardening.

scholarly journals On equivalence and spectral multiplicity of some Gaussian processes

2002 ◽  
pp. 71-76
Author(s):  
Slobodanka Mitrovic
Keyword(s):  
Hilbert Space ◽  
Stochastic Processes ◽  
Gaussian Processes ◽  
Separable Hilbert Space ◽  
Second Order ◽  
Spectral Multiplicity ◽  
Statistical Problems

In this paper we consider some Gaussian second-order stochastic processes (continuous left and purely nondeterministic), in a separable Hilbert space and analyze conditions for these processes to be equivalent. Also, we connect some results of H. Cramer (from Structural and statistical problems for a class of stochastic processes, Princeton Univ. Press, Princeton, NJ, 1971) concerning the problem of spectral multiplicity.

scholarly journals Existence Results for Vector Mixed Quasi-Complementarity Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Suhel Ahmad Khan ◽  
Naeem Ahmad
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Variational Inequality Problem ◽  
Existence Of Solutions ◽  
Complementarity Problems ◽  
Existence Results ◽  
Variational Inequality Problems ◽  
Inequality Problem ◽  
Quasi Variational Inequality

We introduce strong vector mixed quasi-complementarity problems and the corresponding strong vector mixed quasi-variational inequality problems. We establish equivalence between strong mixed quasi-complementarity problems and strong mixed quasi-variational inequality problem in Banach spaces. Further, using KKM-Fan lemma, we prove the existence of solutions of these problems, under pseudomonotonicity assumption. The results presented in this paper are extensions and improvements of some earlier and recent results in the literature.

CLT for Operator Abel Sums of Random Elements

2008 ◽  
Vol 15 (4) ◽  
pp. 785-792
Author(s):  
Tengiz Shervashidze ◽  
Vaja Tarieladze
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Random Element ◽  
Second Order ◽  
Identity Operator ◽  
Random Elements ◽  
Continuous Operators ◽  
Independent Identically Distributed

Abstract Let (ξ 𝑘)𝑘 ≥ 1 be a sequence of independent, identically distributed second order mean zero random elements in a separable Hilbert space 𝐻 and 𝐴 be an element of a certain class of linear continuous operators 𝐻 → 𝐻 such that ‖𝐴‖ < 1. Denote . We prove that if ‖𝐼 – 𝐴‖ tends to zero, where 𝐼 is the identity operator, then the normalized sum (𝐼 – 𝐴2)1/2 η 𝐴 converges in distribution to a Gaussian random element.

scholarly journals Second-order neutral stochastic evolution equations with heredity

2004 ◽  
Vol 2004 (2) ◽  
pp. 177-192 ◽  
Author(s):  
Mark A. McKibben
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Second Order ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Integro Differential Equation ◽  
Real Separable Hilbert Space

Existence, continuous dependence, and approximation results are established for a class of abstract second-order neutral stochastic evolution equations with heredity in a real separable Hilbert space. A related integro-differential equation is also mentioned, as well as an example illustrating the theory.

Evolution Problems with Time-Dependent Subdifferential Operators

2020 ◽  
pp. 1-39 ◽  
Author(s):  
Charles Castaing ◽  
Manuel D. P. Monteiro Marques ◽  
Soumia Saïdi
Keyword(s):  
Time Dependent ◽  
Evolution Problems ◽  
Subdifferential Operators

QUASI-VARIATIONAL INEQUALITIES IN TRANSPORTATION NETWORKS

2004 ◽  
Vol 14 (10) ◽  
pp. 1541-1560 ◽  
Author(s):  
LAURA SCRIMALI
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Transportation Networks ◽  
User Equilibrium ◽  
Equivalent Formulation ◽  
Equilibrium Conditions ◽  
Delay Effects ◽  
Quasi Variational Inequality

This paper aims to consider user equilibrium problems in transportation networks in the most complete and realistic situations. In fact, the presented model allows for the dependence of data on time, the presence of elastic travel demands, the capacity restrictions and delay effects. The equilibrium conditions for such a model are given and the equivalent formulation in terms of a quasi-variational inequality is discussed. Moreover, a theorem for the existence of solutions is shown and a numerical example is provided. Finally, some questions of stability are studied.

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