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Exact controllability for semilinear wave equations. (English) Zbl 0959.93029
The authors study the exact controllability of the system ${\partial^2 y(t, x) \over \partial t^2} - \Delta y(t, x) = f(y(t, x)) + \chi_\omega(x)u(t, x)$ in an $$n$$-dimensional domain $$\Omega$$ with Dirichlet boundary condition, where $$\chi_\omega(x)$$ is the characteristic function of a subdomain $$\omega \subseteq \Omega.$$ Available results require linear growth of the nonlinearity $$f,$$ except in space dimension $$n = 1.$$ The author shows that for general $$n$$ the system is exactly controllable under the superlinear growth condition $$f(s) = o(|s|\sqrt{\ln |s|})$$ as $$s \to \infty.$$

##### MSC:
 93C20 Control/observation systems governed by partial differential equations 93B05 Controllability 93C10 Nonlinear systems in control theory
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##### References:
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