---

＜電子ブック＞
Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I : Abstract Theory / by Atsushi Yagi
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2021.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2021
大きさ	X, 61 p. 17 illus : online resource
著者標目	*Yagi, Atsushi author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Functional analysis LCSH:Measure theory FREE:Differential Equations FREE:Functional Analysis FREE:Measure and Integration
一般注記	1.Preliminary -- 2.Asymptotic Convergence -- 3.Extended Łojasiewicz–Simon Gradient Inequality The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–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 Łojasiewicz–Simon gradient inequality. In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz–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 HTTP:URL=https://doi.org/10.1007/978-981-16-1896-3

 類似資料