An inverse problem for pseudoparabolic equation of filtration: the existence, uniqueness and regularity

Abstract

In this article, we study the inverse problem on the identification of the leading coefficient of the multi-dimensional pseudoparabolic equation. The existence and the uniqueness of its strong solution are proved. The regularity of the solution is also investigated. These results cover the identification of the coefficient of piezo-conductivity for the multi-dimensional model equation of filtration.

Keywords:

• filtration
• inverse problems for PDE
• pseudoparabolic equation
• regularity of solutions
• local existence and uniqueness theorems

AMS Subject Classifications::

• 35B65
• 35K20
• 35K70
• 35Q35
• 35R30
• 76S05