Ασθενείς λύσεις και λύσεις μέτρου σε μη γραμμικές μερικές διαφορικές εξισώσεις

Γεωργιάδης, Στέφανος; Georgiadis, Stefanos

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