Flatness for a Strongly Degenerate 1-D Parabolic Equation

Abstract

We consider the degenerate equation $$\partial \_tf(t,x)-\partial \_x\left(x^{\alpha }\partial \_xf\right)(t,x)=0,$$ on the unit interval $x\in (0,1)$, in the strongly degenerate case $\alpha \in [1,2)$ with adapted boundary conditions at $x=0$ and boundary control at $x=1$. We use the flatness approach to construct explicit controls in some Gevrey classes steering the solution from any initial datum $f\_0\in L^2(0,1)$ to zero in any time $T\textgreater{}0$.

References in corpus (1)

• Null controllability of one-dimensional parabolic equations by the flatness approach