Null controllability from the exterior of fractional parabolic-elliptic coupled systems
We analyze the null controllability properties from the exterior of two parabolic-elliptic coupled systems governed by the fractional Laplacian $(-d_x^2)^s$, $s\in(0,1)$, in one space dimension. In each system, the control is located on a non-empty open set of $\mathbb{R}\setminus(0,1)$. Using t...
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| Format: | Article |
| Language: | English |
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Texas State University
2020-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/26/abstr.html |
| Summary: | We analyze the null controllability properties from the exterior of two
parabolic-elliptic coupled systems governed by the fractional Laplacian
$(-d_x^2)^s$, $s\in(0,1)$, in one space dimension. In each system, the control
is located on a non-empty open set of $\mathbb{R}\setminus(0,1)$.
Using the spectral theory of the fractional Laplacian and a unique continuation
principle for the dual equation, we show that the problem is null controllable
if and only if 1/2<s<1. |
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| ISSN: | 1072-6691 |