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Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I = Abstract Theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I/ by Atsushi Yagi.
Reminder of title:	Abstract Theory /
Author:	Yagi, Atsushi.
Description:	X, 61 p. 17 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-981-16-1896-3
ISBN:	9789811618963

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I = Abstract Theory /
Yagi, Atsushi.

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality IAbstract Theory /[electronic resource] :by Atsushi Yagi. - 1st ed. 2021. - X, 61 p. 17 illus.online resource. - SpringerBriefs in Mathematics,2191-8201. - SpringerBriefs in Mathematics,.

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.

ISBN: 9789811618963

Standard No.: 10.1007/978-981-16-1896-3doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I = Abstract Theory /
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