Christianson, Hans;
Wang, Jian;
Wang, Ruoyu PT;
(2024)
Control Estimates for 0th-Order Pseudodifferential Operators.
International Mathematics Research Notices (IMRN)
, 2024
(8)
pp. 6656-6679.
10.1093/imrn/rnad248.
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Abstract
We introduce the control conditions for 0th order pseudodifferential operators P whose real parts satisfy the Morse–Smale dynamical condition. We obtain microlocal control estimates under the control conditions. As a result, we show that there are no singular profiles in the solution to the evolution equation (i∂t − P)u = f when P has a damping term that satisfies the control condition and f ∈ C∞. This is motivated by the study of a microlocal model for the damped internal waves.
| Type: | Article |
|---|---|
| Title: | Control Estimates for 0th-Order Pseudodifferential Operators |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imrn/rnad248 |
| Publisher version: | https://doi.org/10.1093/imrn/rnad248 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10181498 |
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