Improperly Posed Problems and Their Numerical Treatment: Conference Held at the Mathematisches Forschungsinstitut, Oberwolfach, September 26-October 2

ISBN-13: 9783034854627 / Angielski / Miękka / 2014 / 264 str.

Prof Dr G. Hammerlin; Prof Dr K. Hoffmann

Opis

Whilst improperly posed problems appear in several branches of applied and pure mathematics, this conference concentrated mainly on the practical treatment of ill- posedness. The participants came from 12 countries. The interchange of ideas reflected the spectrum of questions arising in connection with the subject of the conference, where currently progresses in research are made. This volume contains 17 papers presented at the con- ference. Focal points in the programme were: Problems of regularisation, parameter identification, free boundary and inverse problems in differential equations and inte- gral equations of the first kind. Problems, which appear in science, in technical fields and in medicine are dis- cussed as well as general operator equations. In a jOint discussion, several open problems have been worked out which are collected at the end of the volume. The editor's thanks go to all contributors and parti- cipants who made the conference a success; to the manage- ment of the institute with its unique atmosphere; to the Birkhauser Verlag for the possibility to publish the vo- lume in the well-known ISNM series; to Dr. P. Jochum (Mlin- chen) for assistance in organization and to Mrs. Chr. Rogg (Augsburg) for her excellent typing of several manuscripts.

Spis treści

A Stable Marching Scheme for an Ill-Posed Initial Value Problem.- Stability of Parameters Estimated by the Output Least Square Method.- Analytic and Numerical Methods in the Study of the Inverse Scattering Problem for Acoustic Waves.- A Numerical Method for Solving the Inverse Stefan Problem in two Space Variables.- On a Constrained Fourier Extrapolation Method for Numerical Deconvolution.- On the Convergence of Regularization Methods for Ill-Posed Linear Operator Equations.- Comments on Morozov’s Discrepancy Principle.- Reconstruction of a Free Boundary.- The Finite Element Method for a Class of Improperly Posed Integral Equations.- Maxwell’s Equations with Incident Waves as a Field Source.- The Identification of Kinetical Parameters in Medical Receptor Analysis.- Regularizing the Cauchy Problem for the Heat Equation by Sign Restrictions.- Numerical Solution of Fujita’s Equation.- On the Order of Regularization Methods.- Free Boundary Problem for a Non-Linear System of Parabolic Equations, Including One with Reversed Time.- Regularisierungsverfahren für Gleichungen Erster Art mit Positiv Definiten Operatoren.- Über Mathematische Methoden der Beobachtungsverarbeitung.