| Abstract: |
| In this talk, we address the Fredholm backstepping for self-adjoint operators in any dimension. This method of stabilization links an equation needing to be stabilized to an already stable equation, via an invertible transformation $T$. This method was until now restricted to 1D. This is because one had to deal with series that do not converge in dimension 2 or higher, due to the growth of the eigenvalues. In this talk, we will see how the introduction of a spectral projection gets rid of these difficulties, and allows us to apply this method to parabolic equations in all dimension. The growth condition of the spectrum and the gap condition is now relaxed. As an application, we establish the rapid stabilization of the heat and fractional heat equation $(-\Delta^s)$ with $s\in(0,1]$ from measurable or open sets in arbitrary dimensions |
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