Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 27 | |
Number of page(s) | 30 | |
DOI | https://doi.org/10.1051/cocv/2024016 | |
Published online | 09 April 2024 |
Unique continuation and observability for a semi-linear parabolic system
1
College of Digital Technology and Engineering Ningbo University of Finance & Economics, Ningbo 315175, PR China
2
Department of Mathematical Sciences University of Cincinnati, Cincinnati, OH 45221, USA
* Corresponding author: guojiezheng@yeah.net
Received:
22
August
2023
Accepted:
27
February
2024
This article is concerned with the unique continuation and observability of a semi-linear parabolic system in a bounded domain Ω with homogeneous Dirichlet boundary conditions. We first study the existence and uniqueness of the L∞-solution to the system when the initial value belongs to L∞(Ω)2. We then build up some observation estimates for this system. As a consequence, we can conclude if two solutions are equal over a nonempty open subset ω ⊂ Ω at some time T > 0, then they coincide over Ω × [0, T].
Mathematics Subject Classification: 35K40 / 93B07 / 35K45
Key words: Observability / unique continuation / semi-linear parabolic system / frequency function
© The authors. Published by EDP Sciences, SMAI 2024
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