Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I - Abstract Theory (Paperback, 1st ed. 2021)

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.

General

Imprint:	Springer Verlag, Singapore
Country of origin:	Singapore
Series:	SpringerBriefs in Mathematics
Release date:	June 2021
First published:	2021
Authors:	Atsushi Yagi
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	61
Edition:	1st ed. 2021
ISBN-13:	978-981-16-1895-6
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Promotions
LSN:	981-16-1895-X
Barcode:	9789811618956

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