Desensitizing controls for semilinear wave equations. (April 2018) - Wu, Jieqiong; Zhu, Xianzheng
Abstract: The desensitizing control problems for semilinear wave equations are studied. When the nonlinearity f satisfies lim | s | → ∞ f ( s ) | s | ln 2 | s | = lim | s | → ∞ f ′ ( s ) ln 2 | s | = 0, we obtain the existence of a control which desensitizes the boundary observation. The proof is based on the combination of fixed-point arguments and explicit observability estimates for the linearized wave equation with a potential that depends on both x and t . The work solves the problem proposed by Tebou (2011) in the one-dimensional setting. For the interior observation, we assume that the nonlinearity is globally Lipschitz, under which the existence of ε -desensitizing controls is proved. Our proof is based on the fixed-point arguments and the unique continuation property.