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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:  October 2021
Revised:  February 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.

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

    Citation:
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