# Measure solutions for semilinear evolution equations with polynomial growth and their optimal control

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1997)

- Volume: 17, Issue: 1-2, page 5-27
- ISSN: 1509-9407

## Access Full Article

top## Abstract

top## How to cite

topN.U. Ahmed. "Measure solutions for semilinear evolution equations with polynomial growth and their optimal control." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 17.1-2 (1997): 5-27. <http://eudml.org/doc/275844>.

@article{N1997,

abstract = {In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.},

author = {N.U. Ahmed},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {semilinear equations; measure solutions; optimal controls; blow up time; generalized solutions; measure-valued solutions; semilinear evolution equations; polynomial nonlinearities; nonlinear quantum mechanics; control problems},

language = {eng},

number = {1-2},

pages = {5-27},

title = {Measure solutions for semilinear evolution equations with polynomial growth and their optimal control},

url = {http://eudml.org/doc/275844},

volume = {17},

year = {1997},

}

TY - JOUR

AU - N.U. Ahmed

TI - Measure solutions for semilinear evolution equations with polynomial growth and their optimal control

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 1997

VL - 17

IS - 1-2

SP - 5

EP - 27

AB - In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.

LA - eng

KW - semilinear equations; measure solutions; optimal controls; blow up time; generalized solutions; measure-valued solutions; semilinear evolution equations; polynomial nonlinearities; nonlinear quantum mechanics; control problems

UR - http://eudml.org/doc/275844

ER -

## References

top- [1] N.U.Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Res. Notes in Math. Ser., 246, Longman Scientific and Technical and John Wiley, London, New York 1991.
- [2] N.U.Ahmed, Optimal control of infinite dimensional systems governed by functional differential inclusions, Discussiones Mathematicae-Differential Inclusions 15 (1995), 75-94. Zbl0824.49007
- [3] N.U.Ahmed, Optimal relaxed controls for nonlinear infinite dimensional stochastic differential inclusions, Optimal Control of Differential Equations, (Ed. N.H.Pavel), Lect. Notes in Pure and Applied Mathematics, MarcelDekker, Inc. 160 (1994), 1-19.
- [4] H.O. Fattorini, A remark on existence of solutions of infinite dimensional noncompact optimal control problems, SIAM Journal on Control and Optimization 35 (4) (1997), 1422-1433. Zbl0901.49002
- [5] H.O. Fattorini, Relaxation theorems, differential inclusions, and Filippov's theorem for relaxed controls in semilinear infinite dimensional systems,Journal of Differential Equations 112 (1994), 131-153. Zbl0806.93028
- [6] R. Larsen, Functional Analysis: An Introduction, Marcel Dekker Inc., New York 1973. Zbl0261.46001
- [7] N. Dunford and J.T. Schwartz, Linear Operators, Part 1, Interscience Publishers Inc., New York 1958.

## Citations in EuDML Documents

top- N.U. Ahmed, Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control
- N.U. Ahmed, Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control
- N.U. Ahmed, Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.