The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
US School Grade: College Graduate Student
Maße
Höhe: 240 mm
Breite: 165 mm
Gewicht
ISBN-13
978-90-6764-319-1 (9789067643191)
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Schweitzer Klassifikation
Chapter 1 Inverse problems for difference operators: inverse problem of spectral analysis for Jacobi matrices; inverse problem for a difference equation with constant coefficients; the problems of determining a difference operator in non-stationary statement; remarks and references. Chapter 2 A priori estimates and the uniqueness of integro-differential equations with operator coefficients: estimates of the Carleman type and their connection with the uniqueness of solutions of inverse problems; estimates for the Schrodinger equation with operator coefficients; remarks and references. Chapter 3 Inverse problems for differential equations: one-dimensional inverse problem for the wave equation in linearized statement; the method of transformation operators; uniqueness in multidimensional inverse problems in nonstationary and spectral statements; remarks and references. Chapter 4 Volterra operator equations and their applications: Volterra operator equations in scales of Banach spaces; non-hyperbolic Cauchy problem for the wave equation; the problem of integral geometry in a strip; the inverse problem of variational calculus; remarks and references. Chapter 5 Foundations of the theory of conditionally well-posed problems: conditional well-posedness lh; well-posedness of difference schemes; variational methods of solution of lh-stable difference schemes; remarks and references. Chapter 6 Theory of stability of difference schemes: statement of the problem and the necessary conditions of finite stability; basic estimates; sufficient stability conditions; estimates of l-stability up to the boundary; convergence theorems; finite stability of two-layer schemes of the canonical form; conditions of stability in terms of the transition operator; remarks and references.
