On nonlinear, nonconvex evolution inclusions

Nikolaos S. Papageorgiou

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

  • Volume: 15, Issue: 1, page 29-42
  • ISSN: 1509-9407

Abstract

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We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, G δ -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.

How to cite

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Nikolaos S. Papageorgiou. "On nonlinear, nonconvex evolution inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 15.1 (1995): 29-42. <http://eudml.org/doc/275925>.

@article{NikolaosS1995,
abstract = {We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, $G_δ$-subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.},
author = {Nikolaos S. Papageorgiou},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {m-accretive operator; integral solution; nonlinear semigroup; extremal solution; strong relaxation theorem; parabolic system; bang-bang type theorems; extremal integral solution; nonlinear evolution inclusion; equicontinuous nonlinear semigroup; multivalued Cauchy problems; nonlinear parabolic distributed parameter control systems},
language = {eng},
number = {1},
pages = {29-42},
title = {On nonlinear, nonconvex evolution inclusions},
url = {http://eudml.org/doc/275925},
volume = {15},
year = {1995},
}

TY - JOUR
AU - Nikolaos S. Papageorgiou
TI - On nonlinear, nonconvex evolution inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1995
VL - 15
IS - 1
SP - 29
EP - 42
AB - We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, $G_δ$-subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.
LA - eng
KW - m-accretive operator; integral solution; nonlinear semigroup; extremal solution; strong relaxation theorem; parabolic system; bang-bang type theorems; extremal integral solution; nonlinear evolution inclusion; equicontinuous nonlinear semigroup; multivalued Cauchy problems; nonlinear parabolic distributed parameter control systems
UR - http://eudml.org/doc/275925
ER -

References

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  12. [12] V. Lakshmikantham, S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, London 1981. Zbl0456.34002
  13. [13] E. Mitidieri, I. Vrabie, Differential inclusions governed by nonconvex perturbations of m-accretive operators, Differ. and Int. Equations 2 (1989), 525-531. Zbl0736.34014
  14. [14] G. Pianigiani, Differential inclusions: The Baire category method, Proc. CIME, Varenna, ed. by A. Cellina, Lecture Notes in Math. No. 1446, Springer-Verlag, Berlin 1990. Zbl0719.34033
  15. [15] A. Tolstonogov, Extreme continuous selectors of multivalued maps and their applications, Preprint SISSA 72M (June, 1991), Trieste, Italy. (Also Soviet Math. Doklady 43 (2) (1991), 481-485). Zbl0784.54024
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  17. [17] E. Zeidler, Nonlinear Functional Analysis and its Applications II, Springer-Verlag, New York 1990. Zbl0684.47029

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