Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations / / Alexander G. Megrabov.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Megrabov, Alexander G.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2012]; ©2003
• Year of Publication: 2012
• Edition: Reprint 2012
• Language: English
• Series: Inverse and Ill-Posed Problems Series , 40
• Physical Description: 1 online resource (230 p.) :; Zahlr. Abb.
• Other title: Frontmatter --; Preface --; Contents --; Introduction --; Chapter 1. Inverse problems for semibounded string with the directional derivative condition given in the end --; Chapter 2. Inverse problems for the elliptic equation in the half-plane --; Chapter 3. Inverse problems of scattering plane waves from inhomogeneous transition layers (half-space) --; Chapter 4. Inverse problems for finite string with the condition of directional derivative in one end --; Chapter 5. Inverse problems for the elliptic equation in the strip --; Chapter 6. Inverse problems of scattering the plane waves from inhomogeneous layers with a free or fixed boundary --; Chapter 7. Direct and inverse problems for the equations of mixed type --; Chapter 8. Inverse problems connected with determination of arbitrary set of point sources --; Bibliography
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110944983; 9783110238570; 9783110238471; 9783110637205
• ISSN: 1381-4524
• DOI: 10.1515/9783110944983
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Alexander G. Megrabov.

Inverse problems are an important and rapidly developing direction in mathematics, mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monograph direct and inverse problems for partial differential equations are considered. The type of equations focused are hyperbolic, elliptic, and mixed (elliptic-hyperbolic). The direct problems arise as generalizations of problems of scattering plane elastic or acoustic waves from inhomogeneous layer (or from half-space). The inverse problems are those of determination of medium parameters by giving the forms of incident and reflected waves or the vibrations of certain points of the medium. The method of research of all inverse problems is spectral-analytical, consisting in reducing the considered inverse problems to the known inverse problems for the Sturm-Liouville equation or the string equation. Besides the book considers discrete inverse problems. In these problems an arbitrary set of point sources (emissive sources, oscillators, point masses) is determined.