Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I: Abstract Theory (Paperback) (ISBN-13: 9789811618956)

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.


Author: Atsushi Yagi
ISBN-10: 981161895X
ISBN-13: 9789811618956
Publisher: Springer
Language: English
Published: 06/01/2021
Pages: 61
Format: Paperback
Weight: 0.25lbs
Size: 9.21h x 6.14w x 0.15d