Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity

E. Casas; O. Kavian; J.-P. Puel

ESAIM: Control, Optimisation and Calculus of Variations (1998)

  • Volume: 3, page 361-380
  • ISSN: 1292-8119

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Casas, E., Kavian, O., and Puel, J.-P.. "Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 361-380. <http://eudml.org/doc/90530>.

@article{Casas1998,
author = {Casas, E., Kavian, O., Puel, J.-P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {elliptic equation; exponential nonlinearity; existence of solutions; optimal control; necessary optimality conditions},
language = {eng},
pages = {361-380},
publisher = {EDP Sciences},
title = {Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity},
url = {http://eudml.org/doc/90530},
volume = {3},
year = {1998},
}

TY - JOUR
AU - Casas, E.
AU - Kavian, O.
AU - Puel, J.-P.
TI - Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 361
EP - 380
LA - eng
KW - elliptic equation; exponential nonlinearity; existence of solutions; optimal control; necessary optimality conditions
UR - http://eudml.org/doc/90530
ER -

References

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  4. [4] M.G. Grandall, P.H. Rabinowitz: Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems. Arch. Rational Mech. Anal., 58 1975, 207-218. Zbl0309.35057MR382848
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  6. [6] Th. Gallouët, F. Mignot, J.P. Puel: Quelques résultats sur le problème -∆u = λeu. C. R. Acad. Sci. Paris, 307, série I, 1988, 289-292. Zbl0697.35048MR958783
  7. [7] I.M. Gelfand: Some problems in the theory of quasi-linear equations. Uspekhi Mat. Nauk, (N.S.), 14 (86), 1959, 87-158 (in russian); Amer. Math. Soc. Transl, (Ser. 2), 29, 1963, 289-292. MR110868
  8. [8] F. Mignot, J.P. Puel: Sur une classe de problèmes non linéaires avec nonlinéarité positive, croissante, convexe. Comm. PDE, 5 (8), 1980, 791-836. Zbl0456.35034MR583604
  9. [9] F. Mignot, J.P. Puel: Solution singulière radiale de -∆u = λeu. C. R. Acad. Sci. Paris, 307, série I, 1988, 379-382. Zbl0683.35032MR965802
  10. [10] D.H. Sattinger: Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J., 21 1972, 979-1000. Zbl0223.35038MR299921
  11. [11] J.C. Saut, B. Scheurer: Sur l'unicité du problème de cauchy et le prolongement unique pour des équations elliptiques à coefficients non localement bornés. J. Diff. Eq., 43 1982, 28-43. Zbl0431.35017MR645635
  12. [12] G. Stampacchia: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier, 15 1965, 189-258. Zbl0151.15401MR192177

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