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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I/ by Atsushi Yagi.
其他題名:	Abstract Theory /
作者:	Yagi, Atsushi.
面頁冊數:	X, 61 p. 17 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Measure and Integration. -
電子資源:	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:

672015
Measure and Integration.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

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