Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects
2018 ◽
Vol 36
(4)
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pp. 1199-1235
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Keyword(s):
Abstract We analyse the controllability problem for a one-dimensional heat equation involving the fractional Laplacian $(-d_x^{\,2})^{s}$ on the interval $(-1,1)$. Using classical results and techniques, we show that, acting from an open subset $\omega \subset (-1,1)$, the problem is null-controllable for $s>1/2$ and that for $s\leqslant 1/2$ we only have approximate controllability. Moreover, we deal with the numerical computation of the control employing the penalized Hilbert Uniqueness Method and a finite element scheme for the approximation of the solution to the corresponding elliptic equation. We present several experiments confirming the expected controllability properties.
2001 ◽
Vol 108
(1)
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pp. 29-64
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2020 ◽
Vol 19
(4)
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pp. 1949-1978
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2007 ◽
Vol 17
(4)
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pp. 437-448
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2015 ◽
Vol 269
(8)
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pp. 2305-2327
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Keyword(s):
1981 ◽
Vol 29
(1)
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pp. 109-113
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1995 ◽
Vol 125
(1)
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pp. 31-61
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2003 ◽
Vol 118
(1)
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pp. 183-190
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