Flatness for a Strongly Degenerate 1-D Parabolic Equation

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 f...

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Bibliographic Details
Published in:arXiv.org 2015-07
Main Author: Moyano, Iván
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary control
Datum (elevation)
Flatness
Steering
Online Access:Get full text
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Summary: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 \(T\textgreater{}0\).
ISSN:2331-8422