Conditional stability in a backward parabolic system

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 .

Keywords:

• backward parabolic system
• conditional stability
• Carleman estimate

AMS Subject Classifications:

• 35R25
• 35K99

Acknowledgments

The authors thank the anonymous referees for valuable comments.