Control and Cybernetics Exact Controllability for the Semilinear String Equation in Non Cylindrical Domains
نویسنده
چکیده
in a non cylindrical domain. This model, without the resistance represented for f(u), is a linearization of Kirchhoff’s equation for small vibrations of a stretched elastic string when the ends are variables, see Medeiros, Limaco, Menezes (2002). We employ a variant, due to Zuazua (1990b), of the Hilbert Uniqueness Method (HUM), idealized by Lions (1988a, b).
منابع مشابه
Finite Dimensional Null Controllability for the Semilinear Heat Equation
ABSTRACI’. We study a finite dimensional version of the null controllability problem for semilinear heat equations in bounded domains R of R” with Dirichlet boundary conditions. The control acts on any open an non-empty subset of R. The question under consideration is the following: given an initial state, a control time t = 2’ and a finite dimensional subspace E of L”(n), is there a control su...
متن کاملShooting Methods for Numerical Solutions of Exact Controllability Problems Constrained by Linear and Semilinear 2-d Wave Equations
Abstract. Numerical solutions of exact controllability problems for linear and semilinear 2-d wave equations with distributed controls are studied. Exact controllability problems can be solved by the corresponding optimal control problems. The optimal control problem is reformulated as a system of equations (an optimality system) that consists of an initial value problem for the underlying (lin...
متن کاملExact Distributed Controllability for the Semilinear Wave Equation
In this paper we generalize the theorems of exact controllability for the linear wave equation with a distributed control to the semilinear case, showing that, given T large enough, for every initial state in a sufficiently small neighbourhood of the origin in a certain function space, there exists a distributed control, supported on a part of a domain, driving the system to rest. Also, if the ...
متن کاملExact Controllability to the Trajectories of the Heat Equation with Fourier Boundary Conditions: the Semilinear Case
This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form ∂y ∂n + f(y) = 0. We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this...
متن کاملExact Controllability to the Trajectories of the Heat Equation with Fourier Boundary Conditions: the Semilinear
This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form ∂y ∂n + f(y) = 0. We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this...
متن کامل