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

Giuseppe Floridia; Hiroshi Takase; Masahiro Yamamoto

doi:10.3934/ipi.2022016

Article Contents

2022, Volume 16, Issue 5: 1163-1178. Doi: 10.3934/ipi.2022016

This issue Previous Article Direct sampling methods for isotropic and anisotropic scatterers with point source measurements Next Article Using the Navier-Cauchy equation for motion estimation in dynamic imaging

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

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

^*Corresponding author: Masahiro Yamamoto
^*Corresponding author: Masahiro Yamamoto

The first author was supported by Istituto Nazionale di Alta Matematica (INdAM), through the GNAMPA Research Project 2020, titled "Problemi inversi e di controllo per equazioni di evoluzione e loro applicazioni", coordinated by G. Floridia.

Received: September 30, 2021

Revised: January 31, 2022

Early access: April 2022

Published: October 2022

The second author was supported by Grant-in-Aid for JSPS Fellows JP20J11497 of Japan Society for the Promotion of Science. The third author was supported by Grant-in-Aid for Scientific Research (A) 20H00117 of Japan Society for the Promotion of Science

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Abstract

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 $ L^2 $-estimate for initial values by boundary data.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35L40.

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References

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