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Publication list for Uecker, Hannes

  • Nonlinear PDEs: A Dynamical Systems Approach
    Base Product Code Keyword List: gsm; GSM; gsm/182; GSM/182; gsm-182; GSM-182
    Print Product Code: GSM/182
    Online Product Code: GSM/182.E
    Title (HTML): Nonlinear PDEs: A Dynamical Systems Approach
    Author(s) (Product display): Guido Schneider; Hannes Uecker
    Affiliation(s) (HTML): Universität Stuttgart, Stuttgart, Germany; Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs.

    The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given.

    The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.

    Book Series Name: Graduate Studies in Mathematics
    Volume: 182
    Publication Month and Year: 2017-10-26
    Copyright Year: 2017
    Page Count: 575
    Cover Type: Hardcover
    Print ISBN-13: 978-1-4704-3613-1
    Online ISBN 13: 978-1-4704-4228-6
    Print ISSN: 1065-7339
    Online ISSN: 1065-7339
    Primary MSC: 35; 37
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    Applied Math?: true
    MAA Book?: false
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    SXG Subject: DE
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/gsm-182
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    Print Add to Cart URL: /some/url/at/AMS/GSM-182
    Electronic Add to Cart URL: /some/url/at/AMS/GSM-182.E
    Exam/Desk Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4228-6&pisbn=978-1-4704-3613-1&epc=GSM/182.E&ppc=GSM/182&title=Nonlinear%20PDEs%3A%20A%20Dynamical%20Systems%20Approach&author=Guido%20Schneider%3B%20Hannes%20Uecker&type=DE
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4228-6&pisbn=978-1-4704-3613-1&epc=GSM/182.E&ppc=GSM/182&title=Nonlinear%20PDEs%3A%20A%20Dynamical%20Systems%20Approach&author=Guido%20Schneider%3B%20Hannes%20Uecker&type=R

    Graduate students and researchers interested in nonlinear dynamics of PDEs.


    The combination of rigor with simultaneous attention to associated real physical systems makes it particularly appealing.

    -- William Satzer, MAA Reviews

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