The Stabilization of the Solution of an inverse Problem for the Pseudoparabolic Equation

Abstract

Abstract The asymptotic behavior of the strong solution to the inverse problem on recovering an unknown coefficient k(t) in a pseudoparabolic equation (u + ηMu) t + Mu + k(t)u = f is investigated. The differential operator M of the second order with respect spacial variables is supposed to be elliptic and selfajoint. It is proved that the solution of the inverse problem stabilizes to the solution of the appropriate stationary inverse problem as t → + ∞.