Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I
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.
Inhaltsverzeichnis zu „Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I “
1.Preliminary.- 2.Asymptotic Convergence.- 3.Extended Lojasiewicz-Simon Gradient Inequality.
Bibliographische Angaben
- Autor: Atsushi Yagi
- 2021, 1st ed. 2021, X, 61 Seiten, Masse: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 981161895X
- ISBN-13: 9789811618956
Sprache:
Englisch
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