Symmetrization and stabilization of solutions of nonlinear elliptic equations /

Symmetrization and stabilization of solutions of nonlinear elliptic equations /

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Bibliographic Details
Author / Creator:	Efendiev, Messoud, author.
Imprint:	Cham, Switzerland : Springer, [2018]
Description:	1 online resource
Language:	English
Series:	Fields Institute monographs, 2194-3079 ; volume 36 Fields Institute monographs ; 36.
Subject:	Differential equations, Elliptic. Differential equations, Nonlinear. Differential equations, Elliptic. Differential equations, Nonlinear.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11718403

Hidden Bibliographic Details
ISBN:	9783319984070 3319984071 9783319984087 331998408X 9783030074913 3030074919 9783319984063 3319984063
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references. Online resource; title from PDF title page (EBSCO, viewed October 23, 2018).
Summary:	This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
Other form:	Print version: Efendiev, Messoud. Symmetrization and stabilization of solutions of nonlinear elliptic equations. Cham, Switzerland : Springer, [2018] 3319984063 9783319984063
Standard no.:	10.1007/978-3-319-98407-0

Description
Summary:	This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
Physical Description:	1 online resource
Bibliography:	Includes bibliographical references.
ISBN:	9783319984070 3319984071 9783319984087 331998408X 9783030074913 3030074919 9783319984063 3319984063
ISSN:	2194-3079 ;