Abstract: In this talk, we focus on the inverse problem of
determining the potential by the Neumann to Dirichlet map
in
the wave equation
in
with
. Here, we establish a Hölder type stability with
exponent
as follows: for any small
, there exists
such that
To mention the previous related work, twenty years ago (1988), using Sylvester
and Uhlmann s method that is well known in inverse problems, Ziqi Sun, and
Alessandrini and Sylvester obtained
Holder stability
As it mentioned in the abstract, we have obtained a nearly Lipschitz type stability estimate under the same condition as Sun.