Exact boundary and distributed controllability of radial damped wave equation
نویسندگان
چکیده
منابع مشابه
Exact 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 of a Non-linear Generalized Damped Wave Equation: Application to the Sine-gordon Equation
In this paper, we give a sufficient conditions for the exact controllability of the non-linear generalized damped wave equation ẅ + ηẇ + γAw = u(t) + f(t, w, u(t)), on a Hilbert space. The distributed control u ∈ L2 and the operator A is positive definite self-adjoint unbounded with compact resolvent. The nonlinear term f is a continuous function on t and globally Lipschitz in the other variabl...
متن کاملBoundary controllability for the quasilinear wave equation
We study the boundary exact controllability for the quasilinear wave equation in the higher-dimensional case. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally exact controllability around the equilibrium under some checkable geometrical conditions. We then establish the globally exact controllability in such a way tha...
متن کاملExact Controllability for a Semilinear Wave Equation with Both Interior and Boundary Controls
The purpose of this paper is to prove the existence of the exact controllability of a semilinear wave equation with both interior and boundary controls. Let Ω be a bounded open subset of Rn with a smooth boundary, let f (y) be an accretive mapping of L2(0,T ;H−1(Ω)) into L2(0,T ;H 0 (Ω)) with respect to a duality mapping J ,D( f ) = L2(0,T ;L2(Ω)) and having at most a linear growth in y. Consid...
متن کاملExact Neumann boundary controllability for problems of transmission of the wave equation
Using the Hilbert Uniqueness Method, we study the problem of exact controllability in Neumann boundary conditions for problems of transmission of the wave equation. We prove that this system is exactly controllable for all initial states in L( ) (H( ))0. 1. Introduction. Throughout this paper, let be a bounded domain (open, connected, and nonempty) in R(n 1) with a boundary ÿ=@ of class C, and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 1998
ISSN: 0021-7824
DOI: 10.1016/s0021-7824(98)80026-3