Representation of the set of mild solutions to the relaxed semilinear differential inclusion

Irene Benedetti; Elena Panasenko

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2006)

  • Volume: 26, Issue: 1, page 143-158
  • ISSN: 1509-9407

Abstract

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We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.

How to cite

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Irene Benedetti, and Elena Panasenko. "Representation of the set of mild solutions to the relaxed semilinear differential inclusion." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 26.1 (2006): 143-158. <http://eudml.org/doc/271136>.

@article{IreneBenedetti2006,
abstract = {We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.},
author = {Irene Benedetti, Elena Panasenko},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {differential inclusion; mild solution; quasi-solution; convexified and perturbed problem; relaxation theorem; convexified problem; perturbation},
language = {eng},
number = {1},
pages = {143-158},
title = {Representation of the set of mild solutions to the relaxed semilinear differential inclusion},
url = {http://eudml.org/doc/271136},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Irene Benedetti
AU - Elena Panasenko
TI - Representation of the set of mild solutions to the relaxed semilinear differential inclusion
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2006
VL - 26
IS - 1
SP - 143
EP - 158
AB - We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.
LA - eng
KW - differential inclusion; mild solution; quasi-solution; convexified and perturbed problem; relaxation theorem; convexified problem; perturbation
UR - http://eudml.org/doc/271136
ER -

References

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  10. [10] K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New-York, Inc. 2000. Zbl0952.47036
  11. [11] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New-York, Inc. 1983. Zbl0516.47023
  12. [12] G. Pianigiani, On the Fundamental Theory of Multivalued Differential Equations, J. Differential Equations 25 (1) (1977), 30-38. Zbl0398.34017
  13. [13] A. Plis, On Trajectories of Orientor Fields, Bull. Acad. Polon. Sci, Ser. Math. 13 (8) (1965) 571-573. Zbl0138.34104
  14. [14] A.A. Tolstonogov, Differential Inclusions in Banach Space, Kluwer Acad. Publishers, Dordrecht 2000. 

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