# Optimal control of semilinear parabolic equations with state-constraints of bottleneck type

Maïtine Bergounioux; Fredi Tröltzsch

ESAIM: Control, Optimisation and Calculus of Variations (1999)

- Volume: 4, page 595-608
- ISSN: 1292-8119

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topBergounioux, Maïtine, and Tröltzsch, Fredi. "Optimal control of semilinear parabolic equations with state-constraints of bottleneck type." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 595-608. <http://eudml.org/doc/90557>.

@article{Bergounioux1999,

author = {Bergounioux, Maïtine, Tröltzsch, Fredi},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal control; pointwise state constraints; semilinear parabolic equations; constraints of bottleneck; Lagrange multipliers; continuous linear programming},

language = {eng},

pages = {595-608},

publisher = {EDP Sciences},

title = {Optimal control of semilinear parabolic equations with state-constraints of bottleneck type},

url = {http://eudml.org/doc/90557},

volume = {4},

year = {1999},

}

TY - JOUR

AU - Bergounioux, Maïtine

AU - Tröltzsch, Fredi

TI - Optimal control of semilinear parabolic equations with state-constraints of bottleneck type

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 1999

PB - EDP Sciences

VL - 4

SP - 595

EP - 608

LA - eng

KW - optimal control; pointwise state constraints; semilinear parabolic equations; constraints of bottleneck; Lagrange multipliers; continuous linear programming

UR - http://eudml.org/doc/90557

ER -

## References

top- [1] M. Bergounioux and F. Tröltzsch, Optimality Conditions and Generalized Bang-Bang Principle for a State Constrained Semi-linear Parabolic Problem. Num. Funct. Anal. Opt. 15 ( 1996) 517-537. Zbl0858.49021MR1404833
- [2] M. Bergounioux and F. Tröltzsch, Optimal Control of Linear Bottleneck Problems. ESAIM: Cont. Optim. Cal. Var. 3 ( 1998) 235-250. Zbl0904.49020MR1632175
- [3] E. Casas, Pontryagin's principle for state-constrained boundary control problems of semilinear parabolic equations. SIAM J. Control Optim. 35 ( 1997) 1297-1327. Zbl0893.49017MR1453300
- [4] J.P. Raymond, Non Linear Boundary Control of Semilinear Parabolic Problems with Pointwise State Constraints. Discrete and Continuons Dynamical Systems 3 ( 1997) 341-370. Zbl0953.49026MR1444199
- [5] J.P. Raymond and H. Zidani, Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations. Appl. Math. Optim., to appear Zbl0922.49013MR1665668
- [6] F. Tröltzsch, Optimality conditions for parabolic control problems and applications, Teubner Texte zur Mathematik, Teubner, Leipzig ( 1984). Zbl0587.49021MR768586
- [7] J. Zowe and S. Kurcyusz, Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5 ( 1979) 49-62. Zbl0401.90104MR526427

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