Solving inverse initial-value, boundary-value problems

There is a growing interest in inverse initial-value, boundary-value (inverse IVBV) problems, and in the development of robust, computationally efficient methods suitable for their solution. Inverse problems are prominent in science and engineering where often an effect is measured and the cause is not known; scientists and engineers observe the response of a system and desire to know the particulars of the system that elicited such a response. IVBV problems result when the equations that govern the behavior of a system are partial differential equations (wave phenomena, diffusion, potential of all kinds, etc.). Thus, inverse IVBV problems stem from systems governed by partial differential equations in which a response has been measured and a characteristic of the system must be computed. In this paper, an approach to solving inverse IVBV problems is presented in which the stated problem is transformed into a nonlinear optimization problem which is then solved using a genetic algorithm. Results are presented demonstrating the effectiveness of this approach for solving inverse problems, that result from systems governed by three specific partial differential (1) the heat equation, (2) the wave equation, and (3) Poisson's equation. (C) 2001 Elsevier Science Ltd. All rights reserved.