dc.contributor.author | Γεωργιάδης, Στέφανος![]() |
el |
dc.contributor.author | Georgiadis, Stefanos![]() |
en |
dc.date.accessioned | 2019-07-23T11:30:24Z | |
dc.date.available | 2019-07-23T11:30:24Z | |
dc.date.issued | 2019-07-23 | |
dc.identifier.uri | https://dspace.lib.ntua.gr/xmlui/handle/123456789/49132 | |
dc.identifier.uri | http://dx.doi.org/10.26240/heal.ntua.16665 | |
dc.rights | Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/gr/ | * |
dc.subject | Μερικές διαφορικές εξισώσεις | el |
dc.subject | Μη γραμμικές μερικές διαφορικές εξισώσεις | el |
dc.subject | Ασθενείς λύσεις | el |
dc.subject | Λύσεις μέτρου | el |
dc.subject | Συναρτησιακή ανάλυση | el |
dc.subject | Partial differential equations | en |
dc.subject | Nonlinear partial differential equations | en |
dc.subject | Weak solutions | en |
dc.subject | Measure-valued solutions | en |
dc.subject | Functional analysis | en |
dc.title | Ασθενείς λύσεις και λύσεις μέτρου σε μη γραμμικές μερικές διαφορικές εξισώσεις | el |
dc.title | Weak and measure-valued solutions to nonlinear partial differential equations | en |
heal.type | bachelorThesis | |
heal.classification | Μερικές Διαφορικές Εξισώσεις | el |
heal.language | el | |
heal.access | free | |
heal.recordProvider | ntua | el |
heal.publicationDate | 2019-06-27 | |
heal.abstract | The main goal of this dissertation is the study of existence and uniqueness issues of weak solutions in nonlinear partial differential equations. Moreover, we present some collateral results that we found interesting. Apart from presenting the results, we wanted to pay attention to their proofs, writing them down carefully and rigorously, using methods of (nonlinear) functional analysis. More precisely, the dissertation has four parts: (i) The first part is dedicated to elliptic problems. Starting with the basics of linear theory, we introduce a first type of nonlinear problem: variational inequalities. We, then, deal with nonlinear equations and attack some questions of regularity and uniqueness. (ii) In the second part, we study parabolic problems. Again, as in part one, we introduce linear and nonlinear theory and we present some really interesting results on the asymptotic behaviour of the solutions. (iii) Part three contains some modern notions of nonlinear partial differential equations: measure-valued solutions. What is more, we introduce the proper framework for such solutions, which is the concept of Young measures. (iv) The dissertation ends with a short appendix in part four, in which we have the chance to say a few things about the functional analysis tools that we have used in the rest of the text. | en |
heal.advisorName | Χαραλαμπόπουλος, Αντώνιος | el |
heal.committeeMemberName | Χαραλαμπόπουλος, Αντώνιος | el |
heal.committeeMemberName | Κυριάκη, Κυριακή | el |
heal.committeeMemberName | Γκιντίδης, Δρόσος | el |
heal.academicPublisher | Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών. Τομέας Μαθηματικών | el |
heal.academicPublisherID | ntua | |
heal.numberOfPages | 137 σ. | |
heal.fullTextAvailability | true |
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