Abstract parabolic evolution equations and Łojasiewicz-Simon inequality. II, Applications / Atsushi Yagi.
2021
QA377.3 .Y34 2021eb
Linked e-resources
Linked Resource
Online Access
Concurrent users
Unlimited
Authorized users
Authorized users
Document Delivery Supplied
Can lend chapters, not whole ebooks
Details
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
9811626634 (electronic bk.)
9811626626
9789811626623
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.
Linked Resources
Online Access
Record Appears in
Online Resources > Ebooks
All Resources
All Resources
Table of Contents
Preliminaries
Review of Abstract Results
Parabolic Equations
Epitaxial Growth Model
Chemotaxis Model.
Review of Abstract Results
Parabolic Equations
Epitaxial Growth Model
Chemotaxis Model.