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

Resumen


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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