Abstract parabolic evolution equations and Łojasiewicz-Simon inequality. II, Applications / Atsushi Yagi.
Yagi, Atsushi, 1951-
2021
QA377.3 .Y34 2021eb
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Title Abstract parabolic evolution equations and Łojasiewicz-Simon inequality. II, Applications / Atsushi Yagi.
Author Yagi, Atsushi, 1951-
ISBN 9789811626630 (electronic bk.)
9811626634 (electronic bk.)
9811626626
9789811626623
DOI https://doi.org/10.1007/978-981-16-2663-0
Publication Details Singapore : Springer, 2021.
Language English
Description 1 online resource
Item Number 10.1007/978-981-16-2663-0 doi
Call Number QA377.3 .Y34 2021eb
Dewey Decimal Classification 515/.35
Summary 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 and 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 egel equations in one-, two-, and three-dimensional spaces. 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed August 19, 2021).
Series SpringerBriefs in mathematics, 2191-8201
Available in Other Form Abstract parabolic evolution equations and Łojasiewicz-Simon inequality. II, Applications.
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Preliminaries
Review of Abstract Results
Parabolic Equations
Epitaxial Growth Model
Chemotaxis Model.

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