Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality I : Abstract Theory / Atsushi Yagi.
Yagi, Atsushi, 1951- author.
2021
QA377.3 .Y34 2021
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Title Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality I : Abstract Theory / Atsushi Yagi.
Author Yagi, Atsushi, 1951- author.
ISBN 9789811618963 (electronic book)
9811618968 (electronic book)
9789811618970 (print)
9811618976
981161895X (print)
9789811618956 (print)
DOI https://doi.org/10.1007/978-981-16-1896-3
Published Singapore : Springer Singapore Pte. Limited, [2021]
Language English
Description 1 online resource (68 pages)
Item Number 10.1007/978-981-16-1896-3 doi
Call Number QA377.3 .Y34 2021
Dewey Decimal Classification 515/.35
Summary 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.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from digital title page (viewed on June 17, 2021).
Series SpringerBriefs in mathematics.
Available in Other Form Abstract Parabolic Evolution Equations and Łojasiewicz-Simon Inequality I.
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1. Preliminary
2. Asymptotic Convergence
3. Extended Łojasiewicz-Simon Gradient Inequality.

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