A Carleman estimate and an energy method for a first-order symmetric hyperbolic system-Reference-Cited by-同舟云学术

A Carleman estimate and an energy method for a first-order symmetric hyperbolic system

Published:2022 Issue:5 Volume:16 Page:1163
ISSN:1930-8337
Container-title:Inverse Problems and Imaging
language:
Short-container-title:IPI

Author:

Floridia Giuseppe¹²,Takase Hiroshi³,Yamamoto Masahiro⁴⁵⁶

Affiliation:

1. Mediterranean University of Reggio Calabria, Department PAU, Via dell'Università 25 89124 Reggio Calabria, Italy

2. INdAM Unit, University of Catania, Italy

3. Institute of Mathematics for Industry, Kyushu University, Motooka, Nishi-ku, Fukuoka 819-0395, Japan

4. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8914, Japan

5. Honorary Member of Academy of Romanian Scientists, Ilfov, nr. 3, Bucuresti, Romania

6. Correspondence member of Accademia Peloritana dei Pericolanti, Piazza S. Pugliatti 1, 98122 Messina, Italy

Abstract

<p style='text-indent:20px;'>For a symmetric hyperbolic system of the first order, we prove a Carleman estimate under some positivity condition concerning the coefficient matrices. Next, applying the Carleman estimate, we prove an observability <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-estimate for initial values by boundary data.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Control and Optimization,Discrete Mathematics and Combinatorics,Modeling and Simulation,Analysis

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