Boletín SEMA, No 28 (2004)

Tamaño de la letra:  Pequeña  Mediana  Grande

Recent Progress on Exact Controllability Theory of the Wave and Plate Equations

X. Zhang


In this paper, we survey some recent results on (global) exact boundary and/or internal controllability problem for the wave and plate equations, for both linear and semi-linear case. For the semi-linear case, the nonlinearity may be globally Lipschitz continuous, or more generally, satisfy some super-linear growth condition at infinity. Via the duality argument, the problem is reduced to the obtention of suitable uniform observability inequalities for the dual linear and/or linearized system, with respect to the coefficients of its lower order terms. The later is solved by means of a delicate point-wise estimate for the related principal operator and a global Carleman-type estimate.

Key words: Exact controllability, wave equation, plate equation, duality argument, observability inequality, global Carleman estimate.

AMS subject classifications: Primary 93B05; Secondary 93B07, 35B37, 70Q05.

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