SpringerBriefs in Mathematics

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I

Abstract Theory

Authors: Yagi, Atsushi

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  • Makes an extended version of the Łojasiewicz–Simon inequality more available to certain concrete problems
  • Offers a unified method to show asymptotic convergence of solutions for nonlinear parabolic equations and systems
  • Covers a range of applications of concrete nonlinear parabolic equations, including the famous Keller–Segel equations
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  • ISBN 978-981-16-1896-3
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About this book

The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz–Simon gradient inequality.
In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz–Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction–diffusion equations with discontinuous coefficients, reaction–diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller–Segel equations even for higher-dimensional ones.

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook 46,00 €
price for Spain (gross)
  • ISBN 978-981-16-1896-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-981-16-1895-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • 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 I
Book Subtitle
Abstract Theory
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
978-981-16-1896-3
DOI
10.1007/978-981-16-1896-3
Softcover ISBN
978-981-16-1895-6
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 61
Number of Illustrations
17 b/w illustrations
Topics