Abstract Parabolic Evolution Equations and Lojasiewicz-simon Inequality: Abstract Theory - Couverture souple

Yagi, Atsushi

 
9789811618956: Abstract Parabolic Evolution Equations and Lojasiewicz-simon Inequality: Abstract Theory
Couverture souple
ISBN 10 : 981161895X ISBN 13 : 9789811618956
Editeur : Springer Verlag, Singapore, 2021

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer Verlag, Singapore
Date d'édition
2021
Langue
anglais
ISBN 10 
981161895X
ISBN 13 
9789811618956
Reliure
Broché
Numéro d'édition
1
Nombre de pages
71
Coordonnées du fabricant
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com

Europaplatz 3,69115 Heidelberg, Germany
Heidelberg
69115
Allemagne