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SpringerBriefs in Mathematics
cover

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II

Applications

Authors: Yagi, Atsushi

  • Demonstrates the asymptotic convergence to stationary solutions for global solutions of abstract parabolic equations
  • Includes n-dimensional semilinear parabolic equations and higher dimensional Keller–Segel equations among its topics 
  • Provides the methodology for presenting extremely precise convergence results 
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eBook 46,00 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: July 30, 2021
  • ISBN 978-981-16-2663-0
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover 57,19 €
price for Spain (gross)
  • Due: July 30, 2021
  • ISBN 978-981-16-2662-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described.
Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more.
Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed.

Buy this book

eBook 46,00 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: July 30, 2021
  • ISBN 978-981-16-2663-0
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover 57,19 €
price for Spain (gross)
  • Due: July 30, 2021
  • ISBN 978-981-16-2662-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II
Book Subtitle
Applications
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2021
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-16-2663-0
DOI
10.1007/978-981-16-2663-0
Softcover ISBN
978-981-16-2662-3
Series ISSN
2191-8198
Edition Number
1
Number of Pages
IX, 128
Number of Illustrations
1 b/w illustrations
Topics