Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Papadopoulos Stefanos
Supervisors info:
Γεράσιμος Μπαρμπάτης Καθηγητής Τμήμα Μαθηματικών Καποδιστριακό
Ιωάννης Στρατής Καθηγητής Τμήμα Μαθηματικών Καποδιστριακό
Απόστολος Γιαννόπουλος Καθηγητής Μαθηματικών Καποδιστριακό
Original Title:
Εφαρμογή της μεθόδου επικλινέστατης καθόδου σε παραβολικά προβλήματα ανώτερης τάξης
Translated title:
The implementation of the method of Steepest Descents in parabolic problems of higher order
Summary:
Initially, in chapter one, we mention some relations which are commonpalce
in the Asymptotic analysis. In the second chapter we study the Watson
lemma and the Laplace method with which we are able to calculate
the asympotic expansions of some functions defined by integrals and are
known as Laplace integrals. The third chapter is devoted to the Method of
Steepest Descents and its implementation to approach the Laplace integrals.
Subsequently in the fourth chapter we solve the heat equation applying
the Fourier Transform. Finally in the last chapter we apply the Fourier
Transform in parabolic problems of higher order, we end up in one type
of integral which we can approach with the aid of the Method of Steepest
Descents and we present the result in case of 2m order equation
Main subject category:
Science
Keywords:
Asymptotic Analysis, Watson Lemma, Laplace Method, Method of Steepest Descents, Parabolic problems
