# On nonlinear, nonconvex evolution inclusions

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

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

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topNikolaos 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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