Methods for Solving Inverse Problems in Mathematical Physics

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The theory of inverse problems for differential equations is being extensively developed within the framework of mathematical physics. In thestudy of the so-called direct problems the solution of a given differential equation or system of equations is realised by means of supplementary conditions, while in inverse problems the equation itself is also unknown. The determination of both the governing equation and its solution necessitates imposing more additional conditions than in related direct problems.
The sources of the theory of inverse problems may be found late in the 19th century or early 20th century. They include the problem of equilibrium figures for the rotating fluid, the kinematic problems in seismology, the inverse Sturm-Liuville problem and more. Newton’s problem of discovering forces making planets move in accordance with Kepler’s laws was one of the first inverse problems in dynamics of mechanical systems solved in the past. Inverse problems in potential theory in which it is required to determine the body’s position, shape and density from available values of its potential have a geophysical origin. Inverse problems of electromagnetic exploration were caused by the necessity to elaborate the theory and methodology of electromagnetic fields in investigations of the internal structure of Earth’s crust.
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Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.
Product Details
Hardcover: 744 pages
Publisher: CRC Press (March 1, 2000)
Language: English
ISBN-10: 0824719875
ISBN-13: 978-0824719876
Product Dimensions: 8.9 x 6.1 x 1.5 inches

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