Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Γεράσιμος Μπαρμπάτης, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Ιωάννης Στρατής, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Δημήτριος Χελιώτης, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Ασυμπτωτικές Εκτιμήσεις για Παραβολικά Προβλήματα Τέταρτης στις Δύο Διαστάσεις
Translated title:
Asymptotic Estimates for fourth Order Parabolic Problems in Two Dimensions
Summary:
In this master thesis we apply the Steepest Descent Method in parabolic problems of fourth order in two dimensions. First, we present the needed notations, such as asymptotic sequences, Watson's lemma, Laplace Integrals, e.t.c., in order to obtain the capability to calculate the asymptotic expansions of functions defined by Laplace integrals and then we present the calculation of those integrals, via the Deepest Descent Method. Then we use the Method to study parabolic problems of high order in one dimension. In the final chapter we apply the method to a fourth order parabolic problems in two dimensions, which is the main result of the thesis.
Main subject category:
Science
Keywords:
asymptotic estimatew, watson's lemma, depest descent method, fourth order parabolic problems in two dimensions, contribution of saddle points in asymptotic estimates
