{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1418"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1418","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΑΣΥΠΤΩΤΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΗΣ ΕΝΕΡΓΕΙΑΣ ΒΙΣΚΟΕΛΑΣΤΙΚΩΝ ΚΥΜΑΤΩΝ","abstract":"THIS THESIS REFERS TO THE ENERGY BEHAVIOUR OF A LINEARIZED VISCOELASTIC MODEL, IN AN ISOTROPIC AND HOMOGENEOUS MEDIUM WITH QUIET PAST, WHOSE VISCOELASTIC BEHAVIOUR IS EXPRESSED BY MEANS OF RELAXATION FUNCTION WHICH DECAY EXPONENTIALLY INTIME. A REGULAR DISTURBANCE WITH COMPACT SUPPORT IS PROPAGATING THROUGH THIS MEDIUM. THE EVOLUTION OF THE DISTURBANCE IS DESCRIBED BY A WELL- POSED CAUCHY PROBLEM FOR AN INTEGRAL -PARTIAL DIFFERENTIAL EQUATION. THE FUNDAMENTAL ENERGY THEOREM STATES THAT THE ENERGY OF THE TRANSVERSE AS WELL AS OF THE LONGITUDINAL WAVE IS PRESERVED (AND CONSEQUENTLY THE TOTAL ENERGY). THE ASYMPTOTIC ANALYSIS OF THE KINETIC AND STRAIN ENERGY INTEGRALS PROVES THE ASYMPTOTIC (AS T -> T ) EQUIPARTITION OF THE TOTAL ENERGY.","abstract_html":"THIS THESIS REFERS TO THE ENERGY BEHAVIOUR OF A LINEARIZED VISCOELASTIC MODEL, IN AN ISOTROPIC AND HOMOGENEOUS MEDIUM WITH QUIET PAST, WHOSE VISCOELASTIC BEHAVIOUR IS EXPRESSED BY MEANS OF RELAXATION FUNCTION WHICH DECAY EXPONENTIALLY INTIME. A REGULAR DISTURBANCE WITH COMPACT SUPPORT IS PROPAGATING THROUGH THIS MEDIUM. THE EVOLUTION OF THE DISTURBANCE IS DESCRIBED BY A WELL- POSED CAUCHY PROBLEM FOR AN INTEGRAL -PARTIAL DIFFERENTIAL EQUATION. THE FUNDAMENTAL ENERGY THEOREM STATES THAT THE ENERGY OF THE TRANSVERSE AS WELL AS OF THE LONGITUDINAL WAVE IS PRESERVED (AND CONSEQUENTLY THE TOTAL ENERGY). THE ASYMPTOTIC ANALYSIS OF THE KINETIC AND STRAIN ENERGY INTEGRALS PROVES THE ASYMPTOTIC (AS T -> T ) EQUIPARTITION OF THE TOTAL ENERGY.","abstract_has_math":false,"creators":["Καρατζοπούλου-Ζαφειροπούλου, Φιλαρέτη","Zafiropoulos, Filareti"],"institution":"University of Patras","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990","date_published":"1990","updated_at":"2026-07-24T02:24:56Z","subjects":["ΑΣΘΕΝΗΣ ΜΝΗΜΗ","ΑΣΥΜΠΤΩΤΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΟΛΟΚΛΗΡΩΜΑΤΩΝ","Βισκοελαστικότητα","ΕΝΕΡΓΕΙΑ ΚΙΝΗΤΙΚΗ-ΕΝΤΑΤΙΚΗ","Ισοκατανομή ενέργειας","ΚΥΜΑ ΕΓΚΑΡΣΙΟ-ΔΙΑΜΗΚΕΣ","Κυματική διάδοση","Ολοκληρωτικές μερικές διαφορικές εξισώσεις","Χαλάρωση","ASYMPTOTIC BEHAVIOUR OF INTEGRALS","ENERGY KINETIC-STRAIN","EQUIPARTITION OF ENERGY","FADING MEMORY","Integral partial differential equations","Relaxation","Viscoelasticity","Wave propagation","WAVE-TRANSVERSE-LONGITUDINAL","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1418"],"render_values":[{"text":"10.12681/eadd/1418","href":"https://doi.org/10.12681/eadd/1418","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1418","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Καρατζοπούλου-Ζαφειροπούλου, Φιλαρέτη","Zafiropoulos, Filareti"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1990"]},{"key":"dc:publisher","label":"Institution","values":["University of Patras","Πανεπιστήμιο Πατρών"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ΑΣΘΕΝΗΣ ΜΝΗΜΗ","ΑΣΥΜΠΤΩΤΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΟΛΟΚΛΗΡΩΜΑΤΩΝ","Βισκοελαστικότητα","ΕΝΕΡΓΕΙΑ ΚΙΝΗΤΙΚΗ-ΕΝΤΑΤΙΚΗ","Ισοκατανομή ενέργειας","ΚΥΜΑ ΕΓΚΑΡΣΙΟ-ΔΙΑΜΗΚΕΣ","Κυματική διάδοση","Ολοκληρωτικές μερικές διαφορικές εξισώσεις","Χαλάρωση","ASYMPTOTIC BEHAVIOUR OF INTEGRALS","ENERGY KINETIC-STRAIN","EQUIPARTITION OF ENERGY","FADING MEMORY","Integral partial differential equations","Relaxation","Viscoelasticity","Wave propagation","WAVE-TRANSVERSE-LONGITUDINAL","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1418","http://hdl.handle.net/10442/hedi/1418"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["THIS THESIS REFERS TO THE ENERGY BEHAVIOUR OF A LINEARIZED VISCOELASTIC MODEL, IN AN ISOTROPIC AND HOMOGENEOUS MEDIUM WITH QUIET PAST, WHOSE VISCOELASTIC BEHAVIOUR IS EXPRESSED BY MEANS OF RELAXATION FUNCTION WHICH DECAY EXPONENTIALLY INTIME. A REGULAR DISTURBANCE WITH COMPACT SUPPORT IS PROPAGATING THROUGH THIS MEDIUM. THE EVOLUTION OF THE DISTURBANCE IS DESCRIBED BY A WELL- POSED CAUCHY PROBLEM FOR AN INTEGRAL -PARTIAL DIFFERENTIAL EQUATION. THE FUNDAMENTAL ENERGY THEOREM STATES THAT THE ENERGY OF THE TRANSVERSE AS WELL AS OF THE LONGITUDINAL WAVE IS PRESERVED (AND CONSEQUENTLY THE TOTAL ENERGY). THE ASYMPTOTIC ANALYSIS OF THE KINETIC AND STRAIN ENERGY INTEGRALS PROVES THE ASYMPTOTIC (AS T -> T ) EQUIPARTITION OF THE TOTAL ENERGY.","ΜΕΛΕΤΑΤΑΙ Η ΕΝΕΡΓΕΙΑΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΕΝΟΣ ΓΡΑΜΜΙΚΟΠΟΙΗΜΕΝΟΥ ΒΙΣΚΟΕΛΑΣΤΙΚΟΥ ΠΡΟΤΥΠΟΥ, ΜΕΣΑ ΣΕ ΕΝΑ ΙΣΟΤΡΟΠΟ ΚΑΙ ΟΜΟΓΕΝΕΣ ΥΛΙΚΟ ΠΟΥ ΠΑΡΟΥΣΙΑΖΕΙ ΗΡΕΜΟ ΠΑΡΕΛΘΟΝ, Η ΔΕ ΔΙΣΚΟΕΛΑΣΤΙΚΗ ΤΟΥ ΣΥΜΠΕΡΙΦΟΡΑ ΠΕΡΙΓΡΑΦΕΤΑΙ ΑΠΟ ΣΥΝΑΡΤΗΣΕΙΣ ΧΑΛΑΡΩΣΗΣ ΠΟΥ ΦΘΙΝΟΥΝ ΕΚΘΕΤΙΚΑ ΜΕ ΤΟ ΧΡΟΝΟ. ΜΕΣΑ Σ' ΑΥΤΟ ΔΙΑΔΙΔΕΤΑΙ ΜΙΑ ΟΜΑΛΗ ΔΙΑΤΑΡΑΧΗ ΜΕ ΣΥΜΠΑΓΗ ΦΟΡΕΑ, ΤΗΣ ΟΠΟΙΑΣ Η ΕΞΕΛΙΞΗ ΠΕΡΙΓΡΑΦΕΤΑΙ ΑΠΟ ΕΝΑ ΚΑΛΟ ΤΟΠΟΘΕΤΗΜΕΝΟ ΠΡΟΒΛΗΜΑ CAUCHY ΓΙΑ ΜΙΑ ΟΛΟΚΛΗΡΩΤΙΚΗ-ΜΕΡΙΚΗ ΔΙΑΦΟΡΙΚΗ ΕΞΙΣΩΣΗ. ΤΟ ΘΕΜΕΛΙΩΔΕΣ ΕΝΕΡΓΕΙΑΚΟ ΘΕΩΡΗΜΑ ΕΚΦΡΑΖΕΙ ΤΗ ΔΙΑΤΗΡΗΣΗ ΤΗΣ ΕΝΕΡΓΕΙΑΣ ΤΟΣΟ ΤΟΥ ΔΙΑΜΗΚΟΥΣ ΟΣΟ ΚΑΙ ΤΟΥ ΕΓΚΑΡΣΙΟΥ ΚΥΜΑΤΟΣ (ΚΑΙ ΚΑΤΑ ΣΥΝΕΠΕΙΑ ΚΑΙ ΤΗΣ ΣΥΝΟΛΙΚΗΣ). Η ΑΣΥΜΠΤΩΤΙΚΗ ΑΝΑΛΥΣΗ ΤΩΝ ΟΛΟΚΛΗΡΩΜΑΤΩΝ ΤΗΣ ΚΙΝΗΤΙΚΗΣ ΚΑΙ ΤΗΣ ΕΝΤΑΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΟΔΗΓΕΙ ΣΤΟ ΣΥΜΠΕΡΑΣΜΑ ΟΤΙ ΚΑΘΩΣ Ο ΧΡΟΝΟΣ T -> Τ Η ΣΥΝΟΛΙΚΗ ΕΝΕΡΓΕΙΑ ΙΣΟΚΑΤΑΝΕΜΕΤΑΙ."]},{"key":"dc:title","label":"Title","values":["ΑΣΥΠΤΩΤΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΗΣ ΕΝΕΡΓΕΙΑΣ ΒΙΣΚΟΕΛΑΣΤΙΚΩΝ ΚΥΜΑΤΩΝ","ASYMPTOTIC BEHAVIOUR OF ENERGY OF VISCOELASTIC WAVES"]}]}],"canonical_facts":{"dc:creator":["Καρατζοπούλου-Ζαφειροπούλου, Φιλαρέτη","Zafiropoulos, Filareti"],"dc:date":["1990"],"dc:description":["THIS THESIS REFERS TO THE ENERGY BEHAVIOUR OF A LINEARIZED VISCOELASTIC MODEL, IN AN ISOTROPIC AND HOMOGENEOUS MEDIUM WITH QUIET PAST, WHOSE VISCOELASTIC BEHAVIOUR IS EXPRESSED BY MEANS OF RELAXATION FUNCTION WHICH DECAY EXPONENTIALLY INTIME. A REGULAR DISTURBANCE WITH COMPACT SUPPORT IS PROPAGATING THROUGH THIS MEDIUM. THE EVOLUTION OF THE DISTURBANCE IS DESCRIBED BY A WELL- POSED CAUCHY PROBLEM FOR AN INTEGRAL -PARTIAL DIFFERENTIAL EQUATION. THE FUNDAMENTAL ENERGY THEOREM STATES THAT THE ENERGY OF THE TRANSVERSE AS WELL AS OF THE LONGITUDINAL WAVE IS PRESERVED (AND CONSEQUENTLY THE TOTAL ENERGY). THE ASYMPTOTIC ANALYSIS OF THE KINETIC AND STRAIN ENERGY INTEGRALS PROVES THE ASYMPTOTIC (AS T -> T ) EQUIPARTITION OF THE TOTAL ENERGY.","ΜΕΛΕΤΑΤΑΙ Η ΕΝΕΡΓΕΙΑΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΕΝΟΣ ΓΡΑΜΜΙΚΟΠΟΙΗΜΕΝΟΥ ΒΙΣΚΟΕΛΑΣΤΙΚΟΥ ΠΡΟΤΥΠΟΥ, ΜΕΣΑ ΣΕ ΕΝΑ ΙΣΟΤΡΟΠΟ ΚΑΙ ΟΜΟΓΕΝΕΣ ΥΛΙΚΟ ΠΟΥ ΠΑΡΟΥΣΙΑΖΕΙ ΗΡΕΜΟ ΠΑΡΕΛΘΟΝ, Η ΔΕ ΔΙΣΚΟΕΛΑΣΤΙΚΗ ΤΟΥ ΣΥΜΠΕΡΙΦΟΡΑ ΠΕΡΙΓΡΑΦΕΤΑΙ ΑΠΟ ΣΥΝΑΡΤΗΣΕΙΣ ΧΑΛΑΡΩΣΗΣ ΠΟΥ ΦΘΙΝΟΥΝ ΕΚΘΕΤΙΚΑ ΜΕ ΤΟ ΧΡΟΝΟ. ΜΕΣΑ Σ' ΑΥΤΟ ΔΙΑΔΙΔΕΤΑΙ ΜΙΑ ΟΜΑΛΗ ΔΙΑΤΑΡΑΧΗ ΜΕ ΣΥΜΠΑΓΗ ΦΟΡΕΑ, ΤΗΣ ΟΠΟΙΑΣ Η ΕΞΕΛΙΞΗ ΠΕΡΙΓΡΑΦΕΤΑΙ ΑΠΟ ΕΝΑ ΚΑΛΟ ΤΟΠΟΘΕΤΗΜΕΝΟ ΠΡΟΒΛΗΜΑ CAUCHY ΓΙΑ ΜΙΑ ΟΛΟΚΛΗΡΩΤΙΚΗ-ΜΕΡΙΚΗ ΔΙΑΦΟΡΙΚΗ ΕΞΙΣΩΣΗ. ΤΟ ΘΕΜΕΛΙΩΔΕΣ ΕΝΕΡΓΕΙΑΚΟ ΘΕΩΡΗΜΑ ΕΚΦΡΑΖΕΙ ΤΗ ΔΙΑΤΗΡΗΣΗ ΤΗΣ ΕΝΕΡΓΕΙΑΣ ΤΟΣΟ ΤΟΥ ΔΙΑΜΗΚΟΥΣ ΟΣΟ ΚΑΙ ΤΟΥ ΕΓΚΑΡΣΙΟΥ ΚΥΜΑΤΟΣ (ΚΑΙ ΚΑΤΑ ΣΥΝΕΠΕΙΑ ΚΑΙ ΤΗΣ ΣΥΝΟΛΙΚΗΣ). Η ΑΣΥΜΠΤΩΤΙΚΗ ΑΝΑΛΥΣΗ ΤΩΝ ΟΛΟΚΛΗΡΩΜΑΤΩΝ ΤΗΣ ΚΙΝΗΤΙΚΗΣ ΚΑΙ ΤΗΣ ΕΝΤΑΤΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΟΔΗΓΕΙ ΣΤΟ ΣΥΜΠΕΡΑΣΜΑ ΟΤΙ ΚΑΘΩΣ Ο ΧΡΟΝΟΣ T -> Τ Η ΣΥΝΟΛΙΚΗ ΕΝΕΡΓΕΙΑ ΙΣΟΚΑΤΑΝΕΜΕΤΑΙ."],"dc:identifier":["10.12681/eadd/1418","http://hdl.handle.net/10442/hedi/1418"],"dc:language":["gre"],"dc:publisher":["University of Patras","Πανεπιστήμιο Πατρών"],"dc:subject":["ΑΣΘΕΝΗΣ ΜΝΗΜΗ","ΑΣΥΜΠΤΩΤΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΟΛΟΚΛΗΡΩΜΑΤΩΝ","Βισκοελαστικότητα","ΕΝΕΡΓΕΙΑ ΚΙΝΗΤΙΚΗ-ΕΝΤΑΤΙΚΗ","Ισοκατανομή ενέργειας","ΚΥΜΑ ΕΓΚΑΡΣΙΟ-ΔΙΑΜΗΚΕΣ","Κυματική διάδοση","Ολοκληρωτικές μερικές διαφορικές εξισώσεις","Χαλάρωση","ASYMPTOTIC BEHAVIOUR OF INTEGRALS","ENERGY KINETIC-STRAIN","EQUIPARTITION OF ENERGY","FADING MEMORY","Integral partial differential equations","Relaxation","Viscoelasticity","Wave propagation","WAVE-TRANSVERSE-LONGITUDINAL","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"dc:title":["ΑΣΥΠΤΩΤΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΗΣ ΕΝΕΡΓΕΙΑΣ ΒΙΣΚΟΕΛΑΣΤΙΚΩΝ ΚΥΜΑΤΩΝ","ASYMPTOTIC BEHAVIOUR OF ENERGY OF VISCOELASTIC WAVES"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:56Z"}