Existence of optimal controls for control systems governed by nonlinear partial differential equations

Marshall Slemrod

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1974)

  • Volume: 1, Issue: 3-4, page 229-246
  • ISSN: 0391-173X

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Slemrod, Marshall. "Existence of optimal controls for control systems governed by nonlinear partial differential equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.3-4 (1974): 229-246. <http://eudml.org/doc/83677>.

@article{Slemrod1974,
author = {Slemrod, Marshall},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3-4},
pages = {229-246},
publisher = {Scuola normale superiore},
title = {Existence of optimal controls for control systems governed by nonlinear partial differential equations},
url = {http://eudml.org/doc/83677},
volume = {1},
year = {1974},
}

TY - JOUR
AU - Slemrod, Marshall
TI - Existence of optimal controls for control systems governed by nonlinear partial differential equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1974
PB - Scuola normale superiore
VL - 1
IS - 3-4
SP - 229
EP - 246
LA - eng
UR - http://eudml.org/doc/83677
ER -

References

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  1. [1] M.G. Crandall - A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math., 11 (1972), pp. 57-94. Zbl0249.34049MR300166
  2. [2] J.L. Lions, Optimal control of systems governed by partial differential equations, Springer-Verlag, New York, 1971. Zbl0203.09001MR271512
  3. [3] J.L. Lions, On some optimization problems for linear parabolic equations, in « Functional analysis and optimization », ed. E. R. Caianiello, Academic Press, New York, 1966, pp. 115-131. Zbl0182.43101MR231026
  4. [4] J.L. Lions, Optimization pour certaines classes d'équations d'évolution non linéaires, Annali di Mat., 72 (1966), pp. 275-294. Zbl0151.15003MR211106
  5. [5] M.G. Crandall - T.M. Liggett, Generation of semigroups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93 (1971), pp. 265-298. Zbl0226.47038MR287357
  6. [6] H. Brezis - A. Pazy, Convergence and approximation of nonlinear operators in Banach spaces, J. Functional Analysis, 9 (1972), pp. 63-74. Zbl0231.47036MR293452
  7. [7] G.F. Webb, Continuous nonlinear perturbations of nonlinear accretive operators in Banach spaces, J. Functional Analysis, 10 (1972), pp. 191-203. Zbl0245.47052MR361965
  8. [8] M.J. Lighthill - G.B. Whitham, On kinematic waves - II : A theory of traffic flow on long crowded roads, Proc. Roy. Soc. (London), 229A (1955), pp. 317-345. Zbl0064.20906MR72606
  9. [9] C.M. Dafermos, private communication. 
  10. [10] M.G. Crandall, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math., 12 (1972), pp. 108-132. Zbl0246.35018MR316925
  11. [11] P. Benilan, Equations d'evolution dans un espace de Banach quelconque et applications, Thesis, Univ. of Paris (Orsay), 1972. Zbl0246.47068
  12. [12] E.B. Lee - L. Markus, Foundations of optimal control theory, J. Wiley, New York, 1967. Zbl0159.13201MR220537
  13. [13] A.J. Plant, A Riemann integrability condition for nonlinear evolution equations submitted to Amer. J. Math. 

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