Flatness for a Strongly Degenerate 1-D Parabolic Equation

We consider the degenerate equation $\partial\_t f(t,x) - \partial\_x \left( x^α \partial\_x f \right)(t,x) =0,$ on the unit interval $x\in(0,1)$, in the strongly degenerate case $α\in [1,2)$ 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 $T\textgreater{}0$.

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