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On the approximate controllability of variational inequalities and others nonlinear parabolic problems

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Publication Date
1991-03-28
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Elsevier
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We show how the approximate controllability of nonlinear parabolic problems may fail although it is a well-known property for linear equations. For the case of the obstacle problem the answer depends on the negativeness of the righ hand side term and for semilinear equations it depends on the sub or superlinear character at the infinity of the nonlinear term.
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J. L. LIONS, El Planeta Tierra, Instituto de España Ed .. Espasa Calpe. Madrid, 1990. J. L. LIONS, Contrôle optimal de systèmes gouvernès par des équations aux dérivées partielles, Dunod,1968. V. BARBU, Optimal control of variational inequalties, Pitman Res. Notes in Math., nº 100, 1984. J. I. DÍAZ, Article détaillé en préparation. H. BREZIS, Problemes Unilatéraux, J. Math. Pures et Appl., 51, 1972, p. 1-168. T. I. SEIDMAN, Invariance of the reachable set under nonlinear perturbations, S.I.A.M. J. Control and Optimization, 25, 1987, p. 1173-1191. L. VERON, Effets régularisants de semigroupes non linéaires dans les espaces de Banach, Annales Fac,des Sciences de Toulouse, I, 1979, p. 171-200. H, BREZIS et A. FRIEDMAN, Nonlinear parabolic equations involving measures as initial conditions,J. Math. Pures et Appl., 62, 1983, p. 73-97. J. HENRY, Étude de la contrôlabilité de certaines équations paraboliques non linéaircs, These d'État,Université Paris-VI
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