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Article overview
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Null controllability of one-dimensional parabolic equations | | Philippe Martin
; Pierre Rouchon
; Lionel Rosier
; | | Date: |
9 Oct 2014 | | Abstract: | We consider linear one-dimensional parabolic equations with space dependent
coefficients that are only measurable and that may be degenerate or singular.
Considering generalized Robin-Neumann boundary conditions at both extremities,
we prove the null controllability with one boundary control by following the
flatness approach, which provides explicitly the control and the associated
trajectory as series. Both the control and the trajectory have a Gevrey
regularity in time related to the $L^p$ class of the coefficient in front of
$u_t$. The approach applies in particular to the (possibly degenerate or
singular) heat equation $(a(x)u_x)_x-u_t=0$ with $a(x)>0$ for a.e. $xin (0,1)$
and $a+1/a in L^1(0,1)$, or to the heat equation with inverse square potential
$u_{xx}+(mu / |x|^2)u-u_t=0$ with $muge 1/4$. | | Source: | arXiv, 1410.2588 | | Services: | Forum | Review | PDF | Favorites | |
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