Carleman Estimates To Solutions Of Direct And Inverse Problems For Hyperbolic Equations

ABSTRACT

A number of phenomena in modern science can be conveniently described in terms

of problem for hyperbolic equation with Carleman estimates to the solution of

inverse problem.

The purpose of this study is to give a survey of the solution of the inverse

problems for hyperbolic equation by Carleman estimates. We extend the results

and prove the Carleman estimate focusing on an inverse problem for a simple

hyperbolic equation. Also we derive the Lipschitz's stability by energy estimate;

we obtain tomographic images by sent x-ray in dierent directions and measured

at different places.