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

Yagi, Atsushi

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.

Détails de l'édition

• 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: 61
• Coordonnées du fabricant: non disponible
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