Identification of the bulk modulus coefficient in the acoustic equation from boundary observation: a sentinel method

Abstract

Abstract In this paper, we consider an acoustic equation with incomplete data, where the bulk modulus coefficient and initial conditions are partially known. Our goal is to get information about the bulk modulus coefficient independently of the initial conditions from boundary observations. To achieve this goal, we apply the sentinel method introduced by J.L. Lions, which is a functional that links the solution to the given problem with a control function and a state observation. We prove that the existence of the sentinel functional is equivalent to a boundary-null controllability problem with constraints on the control. We use the Hilbert uniqueness method to study this controllability problem to establish the control of minimal norm.

Keywords

• Bulk modulus coefficient
• Incomplete data
• Boundary-null controllability problem
• Sentinel method
• Hilbert uniqueness method