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.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
17 s/w Abbildungen
X, 61 p. 17 illus.
Dateigröße
ISBN-13
978-981-16-1896-3 (9789811618963)
DOI
10.1007/978-981-16-1896-3
Schweitzer Klassifikation
1.Preliminary.- 2.Asymptotic Convergence.- 3.Extended Lojasiewicz-Simon Gradient Inequality.
