Flatness for a Strongly Degenerate 1-D Parabolic Equation

Iván Moyano

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arXiv · 1507.05582

Flatness for a Strongly Degenerate 1-D Parabolic Equation

Iván Moyano

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Abstract

We consider the degenerate equation $$\partial\_t f(t,x) - \partial\_x \left( x^{\alpha} \partial\_x f \right)(t,x) =0,$$ 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 $T\textgreater{}0$.

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Iván Moyano. 2015-07-20. Flatness for a Strongly Degenerate 1-D Parabolic Equation. https://arxiv.org/abs/1507.05582

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