We discuss the Carleman estimates and the applications to inverse problems for hyperbolic equations. For Carleman estimates for hyperbolic equations, we need geometric conditions. Moreover, the finite propagation speed of the hyperbolic equation requests a long observation time length, and its critical value is related to the geometry of observation subboundary and subdomains. In other words, our studies for hyperbolic equations are essentially concerned with both the spatial geometry and the resulting observation time. Therefore we will see that our treatments are more subtle than the parabolic equations.

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Inverse Problems by Carleman Estimates for Hyperbolic Equations

  • Masahiro Yamamoto

摘要

We discuss the Carleman estimates and the applications to inverse problems for hyperbolic equations. For Carleman estimates for hyperbolic equations, we need geometric conditions. Moreover, the finite propagation speed of the hyperbolic equation requests a long observation time length, and its critical value is related to the geometry of observation subboundary and subdomains. In other words, our studies for hyperbolic equations are essentially concerned with both the spatial geometry and the resulting observation time. Therefore we will see that our treatments are more subtle than the parabolic equations.