Abstract
We consider a parabolic system with components in a bounded spatial domain
over a time interval
whose principal part is coupled and discuss the backward problem in time of determining initial data
,
from
,
. We prove two conditional stability estimates under suitable a priori boundness assumptions on the solution
:
and
, where
and
. The proof is based on a Carleman estimate with the weight function
with some constant
and a large parameter
.
Acknowledgments
The authors thank the anonymous referees for valuable comments.