Analytic Semigroups: Applications to Inverse Problems for Flexible Structures
Abstract
In this presentation we consider abstract inverse problems in a least squares formulation for parameter dependent partial differential equations. We are interested in approximation ideas which lead to viable computational techniques for such problems. We pursue our investigations in the context of the general framework for convergence and stability developed by Banks and Ito. Motivated by questions related to the use of accelerometer data to estimate parameters in flexible structures, we focus on second order (in time) systems with sufficient damping so that the system can be modeled by a analytic semigroup. We state and prove a new approximation result (a Trotter-Kato type theorem) for analytic semigroups. This theorem gives conditions under which a family of approximating semigroups and all its time derivatives converges to a limit semigroup and all its time derivatives, respectively. These theoretical results are then stated in terms of simple, readily checked conditions on the sesquilinear forms defining 'stiffness' and 'damping' in the abstract second order systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1990
- Accession Number
- ADA223151
Entities
People
- D. A. Rebnord
- H. Thomas Banks