Using the tools of topological optimization, we propose a method for the location of pollution in the porous media. Thus we propose a modeling of the problem and we study the nonlinear partial differential equation arising in the model.
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References
S. AMSTUTZ, Aspects théoriques et num ériques en optimisation de forme topologique, Thèse de Doctorat n d’ordre 709, INSA Toulouse 2003.
C. BAIOCCHI and A. CAPELO, Variational and quasivariational inequalities applications to free boundary problems, Wiley-Interscience, 1984.
J. C ÉA, Conception optimale, ou identification de forme, calcul rapide de la dérivée directionnelle de la fonction coût, M.A.A.N. 20(3), pp. 371-402, 1986.
R. DAUTRAY and J.L. LIONS, Analyse mathématiques et calcul numérique pour les sciences et les techniques, Volume 2, Masson, 1987.
L.C. EVANS, Partial Differential Equation, Graduate Studies in Mathematics, Volume 19, AMS, 2002.
I. FAYE and D. SECK, Optimal design in thermo elasticity problems, preprint in 2007 UCAD.
S. GARREAU, Ph GUILLAUME and M. MASMOUDI, The topological asymptotic for PDE systems: the elastic case, SIAM J. Control optim. 39(6), pp. 1756-1778, 2001.
Ph. GUILLAUME and K. SIDIDRIS, The topological expansion for the Dirichlet problem, SIAM J. Control optim. 41(4), pp. 1042-1072, 2002.
N. S. LANDKOF, Foundations of Modern Potential Theory, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Band 180, AMS Subject Classification, 1970.
J.L. LIONS, Sur quelques questions d’analyse, de mécanique et de contrôle optimal, Les presses de l’Université de Montreal, 1976.
M. MASMOUDI, The topological Casymptotic, in computational methods for control applications, H. Kawarada and J. Periaux, eds., GAKUTO Internat. Ser. Math. Sci. Appl. Gakkotosho, Tokyo, 2002.
M. NGOM and D. SECK, Detection of tumors by shape and topological opti- mization, preprint in 2007, UCAD.
S.A. NAZAROV and J. SOKOLOWSKI, Asyptotic analysys of Shape Functionnals, J. Math. Pures Appl. 82, pp 125-196, 2003.
R.J. SCHOTTING, Mathematical Aspects of Sault Transport in Porous Media, Thesis of Techniische Universiteit Delft, Rotterdam, PROEFSCHRIFT, 1998.
A. SY and D. Seck, Topological optimization with the p-Laplacian operator: an application in image processing, preprint in 2007, UCAD.
J. TOUMA, Modèle pour tester la représentativité des caractéristiques hydrodynamiquesd’un sol non saturé déterminées in-situ, décembre 1987.
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Faye, I., Sy, A., Seck, D. (2008). On Topological Optimization and Pollution in Porous Media. In: Konaté, D. (eds) Mathematical Modeling, Simulation, Visualization and e-Learning. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74339-2_14
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DOI: https://doi.org/10.1007/978-3-540-74339-2_14
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