Periodic solutions of evolution problem associated with moving convex sets

Charles Castaing; Manuel D.P. Monteiro Marques

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1995)

  • Volume: 15, Issue: 2, page 99-127
  • ISSN: 1509-9407

Abstract

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This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form - D u ∈ N C ( t ) ( u ( t ) ) + f ( t , u ( t ) ) where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, N C ( t ) ( u ( t ) ) is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this differential inclusion are stated under various assumptions on the moving convex set C(t) and the perturbation f.

How to cite

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Charles Castaing, and Manuel D.P. Monteiro Marques. "Periodic solutions of evolution problem associated with moving convex sets." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.2 (1995): 99-127. <http://eudml.org/doc/275954>.

@article{CharlesCastaing1995,
abstract = {This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $-Du ∈ N_\{C(t)\}(u(t)) + f(t,u(t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_\{C(t)\}(u(t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this differential inclusion are stated under various assumptions on the moving convex set C(t) and the perturbation f.},
author = {Charles Castaing, Manuel D.P. Monteiro Marques},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {evolution problem; periodic solution; sweeping process; perturbation; Lipschitzean; absolutely continuous; BV solution; multifunctions; subdifferentials; moving convex sets},
language = {eng},
number = {2},
pages = {99-127},
title = {Periodic solutions of evolution problem associated with moving convex sets},
url = {http://eudml.org/doc/275954},
volume = {15},
year = {1995},
}

TY - JOUR
AU - Charles Castaing
AU - Manuel D.P. Monteiro Marques
TI - Periodic solutions of evolution problem associated with moving convex sets
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1995
VL - 15
IS - 2
SP - 99
EP - 127
AB - This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $-Du ∈ N_{C(t)}(u(t)) + f(t,u(t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_{C(t)}(u(t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this differential inclusion are stated under various assumptions on the moving convex set C(t) and the perturbation f.
LA - eng
KW - evolution problem; periodic solution; sweeping process; perturbation; Lipschitzean; absolutely continuous; BV solution; multifunctions; subdifferentials; moving convex sets
UR - http://eudml.org/doc/275954
ER -

References

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