LEADER 04511nam 2200793 450 001 9910823661503321 005 20230617013645.0 010 $a3-11-094498-7 024 7 $a10.1515/9783110944983 035 $a(CKB)3390000000034977 035 $a(SSID)ssj0001121817 035 $a(PQKBManifestationID)11650050 035 $a(PQKBTitleCode)TC0001121817 035 $a(PQKBWorkID)11057245 035 $a(PQKB)11706532 035 $a(MiAaPQ)EBC3043809 035 $a(DE-B1597)57166 035 $a(OCoLC)979607416 035 $a(DE-B1597)9783110944983 035 $a(Au-PeEL)EBL3043809 035 $a(CaPaEBR)ebr10776778 035 $a(OCoLC)922946923 035 $a(EXLCZ)993390000000034977 100 $a20030806d2003 uy| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aForward and inverse problems for hyperbolic, elliptic, and mixed type equations /$fA.G. Megrabov 205 $aReprint 2012 210 1$aUtrecht ;$aBoston :$cVSP,$d2003. 215 $a1 online resource (242 pages) $cillustrations 225 0 $aInverse and Ill-Posed Problems Series ;$v40 225 0$aInverse and ill-posed problems series 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-11-062813-9 311 $a90-6764-379-3 320 $aIncludes bibliographical references (pages [221]-230). 327 $tFrontmatter -- $tPreface -- $tContents -- $tIntroduction -- $tChapter 1. Inverse problems for semibounded string with the directional derivative condition given in the end -- $tChapter 2. Inverse problems for the elliptic equation in the half-plane -- $tChapter 3. Inverse problems of scattering plane waves from inhomogeneous transition layers (half-space) -- $tChapter 4. Inverse problems for finite string with the condition of directional derivative in one end -- $tChapter 5. Inverse problems for the elliptic equation in the strip -- $tChapter 6. Inverse problems of scattering the plane waves from inhomogeneous layers with a free or fixed boundary -- $tChapter 7. Direct and inverse problems for the equations of mixed type -- $tChapter 8. Inverse problems connected with determination of arbitrary set of point sources -- $tBibliography 330 $aInverse 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. 606 $aDifferential equations, Partial$xNumerical solutions 606 $aInverse problems (Differential equations)$xNumerical solutions 610 $a. 610 $aDifferential Equations. 610 $aDirect Problems. 610 $aDiscrete Inverse Problems. 610 $aElliptic-Hyperbolic. 610 $aElliptic. 610 $aHyperbolic. 610 $aInverse Problems. 610 $aMixed. 610 $aPartial Differential Equations. 610 $aPoint Sources. 610 $aSpectral-Analytical. 610 $aString Equation. 610 $aSturm-Liouville Equation. 615 0$aDifferential equations, Partial$xNumerical solutions. 615 0$aInverse problems (Differential equations)$xNumerical solutions. 676 $a242 686 $aSK 560$qSEPA$2rvk 700 $aMegrabov$b A. G$01721953 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910823661503321 996 $aForward and inverse problems for hyperbolic, elliptic, and mixed type equations$94121929 997 $aUNINA