Dynamical Inverse Problems of Distributed Systems

✍ Scribed by Vyacheslav I. Maksimov

• Publisher: De Gruyter
• Year: 2002
• Tongue: English
• Leaves: 280
• Series: Inverse and Ill-Posed Problems Series; 37
• Edition: Reprint 2014
• Category: Library

✦ Synopsis

This monograph deals with problems of dynamical reconstruction of unknown variable characteristics (distributed or boundary disturbances, coefficients of operator etc.) for various classes of systems with distributed parameters (parabolic and hyperbolic equations, evolutionary variational inequalities etc.).

✦ Table of Contents

Introduction
Chapter 1. Problems of dynamical modeling in abstract systems
1.1. Reconstruction of inputs in dynamical systems. The method of auxiliary controlled models
1.2. Method of Stabilization of Lyapunov Functionals
1.3. Reconstruction of distributed controls in abstract systems. The case of instantaneous restrictions imposed on controls
Chapter 2. Approximation of inputs in parabolic equations
2.1. Reconstruction of distributed controls in nonlinear parabolic equations
2.2. Approximation of boundary controls in Neumann conditions and of coefficients of the elliptic operator
2.3. Reconstruction of intensities of point sources through results of sensory measurements
2.4. Approximation of boundary controls. The case of Dirichlet boundary conditions
Chapter 3. Approximation of inputs in parabolic variational inequalities
3.1. Dynamical discrepancy method
3.2. The role of a priori information in the problem of control reconstruction. The method of smoothing functional
3.3. Applications to inverse problems of mathematical physics and mechanics
Chapter 4. Finite-dimensional approximation of inputs. Examples
4.1. Reconstruction of boundary controls. The dynamical discrepancy method
4.2. Reconstruction of distributed control. The method of smoothing functional
4.3. Reconstruction of coefficients of the elliptic operators and boundary controls
4.4. The results of computer modeling
Bibliography