Εκτιμήσεις λογαριθμικής ευστάθειας για ένα αντίστροφο πρόβλημα της κυματικής εξίσωσης και μελέτη του ακτινικά συμμετρικού προβλήματος

Μαντούβαλος, Χαράλαμπος; Mantouvalos, Charalampos

dc.contributor.author	Μαντούβαλος, Χαράλαμπος	el
dc.contributor.author	Mantouvalos, Charalampos	en
dc.date.accessioned	2024-06-17T11:31:09Z
dc.date.available	2024-06-17T11:31:09Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/59736
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.27432
dc.description	Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Εφαρμοσμένες Μαθηματικές Επιστήμες”	el
dc.rights	Αναφορά Δημιουργού-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nd/3.0/gr/	*
dc.subject	Αντίστροφα προβλήματα	el
dc.subject	Διαφορικές εξισώσεις	el
dc.subject	Κυματική εξίσωση	el
dc.subject	Συναρτήσεις Bessel	el
dc.subject	Mathematica	en
dc.subject	Εκτίμηση ευστάθειας	el
dc.subject	Stability estimates	en
dc.subject	Dirichlet-to-Neumann map	en
dc.subject	Radon Transform	en
dc.subject	Poincare-Linstedt method	en
dc.title	Εκτιμήσεις λογαριθμικής ευστάθειας για ένα αντίστροφο πρόβλημα της κυματικής εξίσωσης και μελέτη του ακτινικά συμμετρικού προβλήματος	el
dc.title	On Logarithmic stability estimate for an inverse wave problem and on the investigation of the radial symmetric problem	en
heal.type	masterThesis
heal.classification	Μαθηματικά	el
heal.classification	Mathematics	en
heal.classification	Αντίστροφα προβλήματα	el
heal.classification	Inverse problems	en
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2024-03-22
heal.abstract	In chapter 1, we briefly discuss about inverse problems, the differences with direct problems and how one may approach an inverse problem in order to obtain a desired estimate. They arise in various real world problems and applications. In chapter 2, we consider the work of Bellassoued-Choulli-Yamamoto (2009) for finding a sta- bility estimate for an inverse problem of the wave equation and a multidimentional Borg-Levinson theorem from their analytical procedure to produce the log-type stability as it follows in theorems 14, 16 and 17. Their work is mostly based on the properties of the solution of the wave equa- tion and providing a stability estimate for hyperbolic equation for a relatively open subset of the boundary and using generalized X-ray and Fourier transformations. In chapter 3, we present a semi analytical-numerical procedure for verifying theorem 17 for the simplest case where we have the source of the wave equation depending only on the radius, hence we have radial symmetry, and our domain is the circle with radius 1.1. For the analytic part we solve a eigenvalue differential equation with radial symmetry considering the solutions arise from Bessel’s functions. We apply Poincare-Linstedt method to have the perturbed solution familiar with Bessel coefficients, hence we got a matrix with 2 arbitrary constants. For the numerical pro- cedure we used Wolfram Mathematica where we had to find in the graph at least 6 eigenvalues for the two sources q1 and q2. After finding the eigenvalues we could find the eigenfunctions and we applied the Sobolev norm to construct the terms that arise in theorem 17 and we concluded to the verification of the estimate. In chapter 4, we provide an appendix for the basic definitions that are not covered in the pre- vious chapters, and provide some calculations that arise in chapters 2 and 3.	en
heal.advisorName	Χαραλαμπόπουλος, Αντώνιος	el
heal.committeeMemberName	Καραφύλλης, Ιάσων	el
heal.committeeMemberName	Γκιντίδης, Δρόσος	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών	el
heal.academicPublisherID	ntua
heal.numberOfPages	74 σ.	el
heal.fullTextAvailability	false