Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Papachristodoulos Ioannis
Supervisors info:
Κόττα Αθανασιάδου Ευαγγελία, Επίκουρος Καθηγήτρια, Μαθηματικό, Σχολή θετικών επιστημών- Μπαρμπάτης Γεράσιμος, Αναπληρωτής Καθηγητής, Μαθηματικό, Σχολή θετικών επιστημών- Στρατής Ιωάννης, Καθηγητής, Μαθηματικό, Σχολή θετικών επιστημών
Original Title:
Η Θεωρία Riesz-Fredholm για συμπαγείς τελεστές στη μελέτη των προβλημάτων κυματικής σκέδασης.
Translated title:
The Riesz-Fredholm Theory for compact operators on the study of acoustic scattering problems. ”
Summary:
The acoustic scattering problems with time harmonic dependence become boundary value problems for the Helmholtz equation. In this diploma thesis we are studying the well-posedness of these problems using the Riesz-Fredholm Theory for compact operators. We prove solvability using single and double layer potentials while uniqueness is obtained from Rellich Lemma. With single and double layer potentials an acoustic scattering problem is transformed into an integral equation of the second kind for functions defined on the surface of the scatterer. The equivalent integral operators are proved to be compact and therefore we can apply the Riesz-Fredholm Theory on them.
Main subject category:
Science
Other subject categories:
Mathematics
Keywords:
Riesz-Fredholm theory, scattering theory, compact operators
