Free access
Issue
ESAIM: COCV
Volume 15, Number 1, January-March 2009
Page(s) 117 - 138
DOI http://dx.doi.org/10.1051/cocv:2008019
Published online 23 January 2009
  1. L.J. Álvarez-Vázquez, A. Martínez, C. Rodríguez and M.E. Vázquez-Méndez, Numerical convergence for a sewage disposal problem. Appl. Math. Model. 25 (2001) 1015–1024. [CrossRef]
  2. L.J. Álvarez-Vázquez, A. Martínez, C. Rodríguez and M.E. Vázquez-Méndez, Numerical optimization for the location of wastewater outfalls. Comput. Optim. Appl. 22 (2002) 399–417. [CrossRef] [MathSciNet]
  3. L.J. Álvarez-Vázquez, A. Martínez, C. Rodríguez and M.E. Vázquez-Méndez, Mathematical model for optimal control in wastewater discharges: the global performance. C. R. Biologies 328 (2005) 327–336. [CrossRef]
  4. L.J. Álvarez-Vázquez, A. Martínez, R. Muñoz-Sola, C. Rodríguez and M.E. Vázquez-Méndez, The water conveyance problem: Optimal purification of polluted waters. Math. Models Meth. Appl. Sci. 15 (2005) 1393–1416. [CrossRef]
  5. A. Bermúdez, Numerical modelling of water pollution problems, in Environment, Economics and their Mathematical Models, J.I. Diaz and J.L. Lions Eds., Masson, Paris (1994).
  6. A. Bermúdez, C. Rodríguez and M.A. Vilar, Solving shallow water equations by a mixed implicit finite element method. IMA J. Num. Anal. 11 (1991) 79–97. [CrossRef]
  7. E. Casas, Pontryagin's principle for state constrained boundary control problems of semilinear parabolic equations. SIAM J. Control Optim. 35 (1997) 1297–1327. [CrossRef] [MathSciNet]
  8. R. Gibbons, A Primer in Game Theory. Pearson Higher Education (1992).
  9. O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, in Translations of Mathematical Monographs 23, Amer. Math. Soc., Providence (1968).
  10. J.L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux derivées partielles. Dunod, Paris (1968).
  11. J.L. Lions and E. Magenes, Problèmes aux limites non homogenes et applications. Dunod, Paris (1968).
  12. A. Martínez, C. Rodríguez and M.E. Vázquez-Méndez, Theoretical and numerical analysis of an optimal control problem related to wastewater treatment. SIAM J. Control Optim. 38 (2000) 1534–1553. [CrossRef] [MathSciNet]
  13. D. Parra-Guevara and YN. Skiba, Elements of the mathematical modeling in the control of pollutants emissions. Ecol. Model. 167 (2003) 263–275. [CrossRef]
  14. O. Pironneau, Finite Element Methods for Fluids. J. Wiley & Sons, Chichester (1989).
  15. A.M. Ramos, R. Glowinski and J. Periaux, Nash equilibria for the multiobjetive control of linear partial differential equations. J. Optim. Theory Appl. 112 (2002) 457–498. [CrossRef] [MathSciNet]
  16. E. Zeidler, Nonlinear Functional Analysis and its Applications. Springer-Verlag (1993).