Exact controllability for semilinear wave equations
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 \(s \to \infty.\)
scientific article; zbMATH DE number 1542466