Unbounded state-dependent sweeping processes with perturbations in uniformly convex and q-uniformly smooth Banach spaces

Samir Adly; Ba Khiet Le

doi:10.3934/naco.2018005

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2018, Volume 8, Issue 1: 81-95. Doi: 10.3934/naco.2018005

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Unbounded state-dependent sweeping processes with perturbations in uniformly convex and q-uniformly smooth Banach spaces

Samir Adly^1, , and
Ba Khiet Le^2,

1.
XLIM UMR-CNRS 7252, Université de Limoges, 87060 Limoges, France
2.
Centro de Modelamiento Matemático (CMM), Universidad de Chile, Santiago, Chile

* Corresponding author
* Corresponding author

Received: December 2016

Revised: January 2018

Published: March 2018

The second author is supported by Fondecyt Postdoc Project 3150332.

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Abstract

In this paper, the existence of solutions for a class of first and second order unbounded state-dependent sweeping processes with perturbation in uniformly convex and $q$-uniformly smooth Banach spaces are analyzed by using a discretization method. The sweeping process is a particular differential inclusion with a normal cone to a moving set and is of a great interest in many concrete applications. The boundedness of the moving set, which plays a crucial role for the existence of solutions in many works in the literature, is not necessary in the present paper. The compactness assumption on the moving set is also improved.

Keywords:

Unbounded state-dependent sweeping processes,
Differential Inclusions,
Normal cones,
Variational Analysis,
Uniformly Convex and q-Uniformly Smooth Banach Spaces.

Mathematics Subject Classification: 34A60, 49J52, 49J53.

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References

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