04511nam 2200793 450 991082366150332120230617013645.03-11-094498-710.1515/9783110944983(CKB)3390000000034977(SSID)ssj0001121817(PQKBManifestationID)11650050(PQKBTitleCode)TC0001121817(PQKBWorkID)11057245(PQKB)11706532(MiAaPQ)EBC3043809(DE-B1597)57166(OCoLC)979607416(DE-B1597)9783110944983(Au-PeEL)EBL3043809(CaPaEBR)ebr10776778(OCoLC)922946923(EXLCZ)99339000000003497720030806d2003 uy| 0engurcnu||||||||txtccrForward and inverse problems for hyperbolic, elliptic, and mixed type equations /A.G. MegrabovReprint 2012Utrecht ;Boston :VSP,2003.1 online resource (242 pages) illustrationsInverse and Ill-Posed Problems Series ;40Inverse and ill-posed problems seriesBibliographic Level Mode of Issuance: Monograph3-11-062813-9 90-6764-379-3 Includes bibliographical references (pages [221]-230).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 -- BibliographyInverse 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. Differential equations, PartialNumerical solutionsInverse problems (Differential equations)Numerical solutions.Differential Equations.Direct Problems.Discrete Inverse Problems.Elliptic-Hyperbolic.Elliptic.Hyperbolic.Inverse Problems.Mixed.Partial Differential Equations.Point Sources.Spectral-Analytical.String Equation.Sturm-Liouville Equation.Differential equations, PartialNumerical solutions.Inverse problems (Differential equations)Numerical solutions.242SK 560SEPArvkMegrabov A. G1721953MiAaPQMiAaPQMiAaPQBOOK9910823661503321Forward and inverse problems for hyperbolic, elliptic, and mixed type equations4121929UNINA