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

  • *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.

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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  • 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.


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