Existence of optimal controls for control systems governed by nonlinear partial differential equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 1 (1974) no. 3-4, pp. 229-246. 
@article{ASNSP_1974_4_1_3-4_229_0,
     author = {Slemrod, Marshall},
     title = {Existence of optimal controls for control systems governed by nonlinear partial differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {229--246},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 1},
     number = {3-4},
     year = {1974},
     mrnumber = {380560},
     zbl = {0314.49007},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1974_4_1_3-4_229_0/}
}
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
SP  - 229
EP  - 246
VL  - 1
IS  - 3-4
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1974_4_1_3-4_229_0/
LA  - en
ID  - ASNSP_1974_4_1_3-4_229_0
ER  - 
%0 Journal Article
%A Slemrod, Marshall
%T Existence of optimal controls for control systems governed by nonlinear partial differential equations
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1974
%P 229-246
%V 1
%N 3-4
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1974_4_1_3-4_229_0/
%G en
%F ASNSP_1974_4_1_3-4_229_0
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, Série 4, Tome 1 (1974) no. 3-4, pp. 229-246. http://www.numdam.org/item/ASNSP_1974_4_1_3-4_229_0/

[1] M.G. Crandall - A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math., 11 (1972), pp. 57-94. | MR | Zbl

[2] J.L. Lions, Optimal control of systems governed by partial differential equations, Springer-Verlag, New York, 1971. | MR | Zbl

[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. | MR | Zbl

[4] J.L. Lions, Optimization pour certaines classes d'équations d'évolution non linéaires, Annali di Mat., 72 (1966), pp. 275-294. | MR | Zbl

[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. | MR | Zbl

[6] H. Brezis - A. Pazy, Convergence and approximation of nonlinear operators in Banach spaces, J. Functional Analysis, 9 (1972), pp. 63-74. | MR | Zbl

[7] G.F. Webb, Continuous nonlinear perturbations of nonlinear accretive operators in Banach spaces, J. Functional Analysis, 10 (1972), pp. 191-203. | MR | Zbl

[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. | MR | Zbl

[9] C.M. Dafermos, private communication.

[10] M.G. Crandall, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math., 12 (1972), pp. 108-132. | MR | Zbl

[11] P. Benilan, Equations d'evolution dans un espace de Banach quelconque et applications, Thesis, Univ. of Paris (Orsay), 1972.

[12] E.B. Lee - L. Markus, Foundations of optimal control theory, J. Wiley, New York, 1967. | MR | Zbl

[13] A.J. Plant, A Riemann integrability condition for nonlinear evolution equations submitted to Amer. J. Math.