Inverse abstract Cauchy problems

Abstract

We consider direct and inverse abstract Cauchy problems with time-dependent coefficients. We give an explicit representation of the unique solution operator of the direct abstract Cauchy problem. We use the obtained solution and a new method to recover time-dependent coefficients for the inverse abstract Cauchy problem.

Keywords:

• Abstract Cauchy problem
• direct problem
• inverse problem
• variable coefficient

2010 Mathematics Subject Classifications:

• 12H20
• 49J27
• 35R30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors were supported by the Nazarbayev University Program 091019CRP2120. No new data was collected or generated during the course of this research.