Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation

Abstract

We study the global stability in determination of a coefficient in an acoustic equation from data of the solution in a subboundary over a time interval. Providing regular initial data and values of coefficients in a neighbourhood of the boundary, without any assumption on an observation subboundary, we prove the logarithmic stability estimate in the inverse problem with a single measurement. Moreover the exponent in the stability estimate depends on the regularity of initial data.