Inverse problems for the stationary and pseudoparabolic equations of diffusion

ABSTRACT

The identification of an unknown coefficient in the lower term of pseudoparabolic differential equation of diffusion ${(u+\eta Mu)}_t+Mu+ku=f$ and elliptic second-order differential equation $Mu+ku=f$ with the Dirichlet boundary condition is considered. The identification of k is based on an integral boundary data. The local existence and uniqueness of generalized strong solutions for the inverse problems are proved. The stability estimates are exposed.

KEYWORDS:

• Inverse problems for PDE
• boundary value problems
• second-order elliptic equations
• pseudoparabolic equation
• existence and uniqueness theorems

AMS SUBJECT CLASSIFICATIONS:

• 35A01
• 35B30
• 35G16
• 35J25
• 35R30

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Russian Science Foundation [grant number 18-11-00203].