[01629] Constructive approaches for the controllability of semi-linear heat and wave equations

Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602

Type : Contributed Talk

Abstract : We addresses the controllability of the semi-linear heat equation $\partial_t y- \partial_{xx} y+f(y)=0$, $x\in (0,1)$. Assuming that the function $f$ is $C^1$ over $\mathbb{R}$ and $\limsup_{\vert r\vert\to \infty} \vert f^\prime(r)\vert/\ln^{3/2}\vert r\vert\leq \beta$ for some $\beta>0$ small enough, we show that a fixed point application related to a linearized equation is contracting yielding a constructive method to approximate boundary controls for the semi-linear equation. Similar ideas are used to address the controllability for semi-linear wave type equations.