Conditional stability in a backward parabolic system
Oleg Imanuvilov, Masahiro Yamamoto · Applicable Analysis · 2014
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 .