-
Abstract
This paper is concerned with the null-exact controllability of a cascade
system formed by a semilinear heat and a semilinear wave equation
in a cylinder $\Omega \times (0,T)$.
More precisely, we intend to drive the solution of the heat equation
(resp. the wave equation) exactly to zero
(resp. exactly to a prescribed but arbitrary final state).
The control acts only on the heat equation and is supported by a set
of the form $\omega \times (0,T)$, where $\omega \subset \Omega$.
In the wave equation, the restriction of the solution to the heat
equation to another set $\mathcal O \times (0,T)$ appears.
The nonlinear terms are assumed to be globally Lipschitz-continuous.
In the main result in this paper, we show that, under appropriate
assumptions on $T$, $\omega$ and $\mathcal O$, the equations are
simultaneously controllable.
Mathematics Subject Classification: 35M20, 93B05, 93B07.
\begin{equation} \\ \end{equation}
-
Access History
-
{{journal.titleEn}} 
DownLoad: