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＜E-Book＞
Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality II : Applications / by Atsushi Yagi
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2021.
Publisher	(Singapore : Springer Nature Singapore : Imprint: Springer)
Year	2021
Language	English
Size	IX, 128 p. 607 illus : online resource
Authors	*Yagi, Atsushi author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis LCSH:Functional analysis LCSH:Measure theory FREE:Analysis FREE:Functional Analysis FREE:Measure and Integration
Notes	Preliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensionalspaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed HTTP:URL=https://doi.org/10.1007/978-981-16-2663-0

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