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Some results about the approximate controllability property for quasilinear diffusion equations

Díaz Díaz, Jesús Ildefonso and Ramos del Olmo, Ángel Manuel (1997) Some results about the approximate controllability property for quasilinear diffusion equations. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 324 (11). pp. 1243-1248. ISSN 0764-4442

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We study the approximate controllability property for y(t) - Delta phi(y) = u chi(omega), on Omega x (0, T), where Omega is a bounded open set of R-N and omega subset of Omega. First, we show some negative results for the case phi(s) = \s\(m-1)s, 0 < m < 1, by means of an obstruction phenomenon. In a second part, we obtain a positive answer on the space H-1-gamma(Omega), for any gamma > 0, for a class of functions phi essentially linear at infinity, by using a higher order vanishing viscosity argument.

Item Type:Article
Uncontrolled Keywords:quasilinear diffusion equation; approximate controllability
Subjects:Sciences > Mathematics > Differential equations
ID Code:15821

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