Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I / SpringerBriefs in Mathematics (PDF)
Abstract Theory
(Sprache: Englisch)
The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz-Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a...
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The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz-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 Lojasiewicz-Simon gradient inequality.
In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Lojasiewicz-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.
Bibliographische Angaben
- Autor: Atsushi Yagi
- 2021, 1st ed. 2021, 61 Seiten, Englisch
- Verlag: Springer Nature Singapore
- ISBN-10: 9811618968
- ISBN-13: 9789811618963
- Erscheinungsdatum: 31.05.2021
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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- Größe: 0.97 MB
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Englisch
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