Source reconstruction and stability via boundary control of abstract viscoelastic systems

Abstract

We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula and stability estimate for the source in terms of the boundary measurement. Our approach relies on the exact boundary controllability of the corresponding viscoelastic systems for which we also provide a new proof based on a modification of the well-known moment method.

Keywords:

• Inverse source problem
• viscoelasticity
• boundary control
• observability
• reconstruction formula
• moment method

2010 Mathematics Subject Classifications:

• 93B07
• 35R30
• 74D05
• 35L10

Disclosure statement

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