Inverse problems for general parabolic systems and application to Ornstein-Uhlenbeck equation

Abstract

We investigate the link between inverse problems and final state observability for a general class of parabolic systems. We generalize a stability result for initial data due to García and Takahashi [16], known for the case of self-adjoint dissipative operators. More precisely, we consider a system governed by an analytic semigroup. Under the assumption of final state observability, we prove a logarithmic stability estimate depending on the analyticity angle of the semigroup. This is done by using a general logarithmic convexity result. The abstract result is illustrated by considering the Ornstein-Uhlenbeck equation.

14 pages, 2 figures

References in corpus (1)

• Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions

Cited by in corpus (1)

• Logarithmic convexity and impulsive controllability for the 1-D heat equation with dynamic boundary conditions