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Lectures on nonlinear evolution equa...

Racke, Reinhard.

Lectures on nonlinear evolution equationsinitial value problems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on nonlinear evolution equationsby Reinhard Racke.
Reminder of title:	initial value problems /
Author:	Racke, Reinhard.
Published:	Cham :Springer International Publishing :2015.
Description:	viii, 306 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Initial value problems.
Online resource:	http://dx.doi.org/10.1007/978-3-319-21873-1
ISBN:	9783319218731$q(electronic bk.)

Lectures on nonlinear evolution equationsinitial value problems /
Racke, Reinhard.

Lectures on nonlinear evolution equationsinitial value problems /[electronic resource] :by Reinhard Racke. - 2nd ed. - Cham :Springer International Publishing :2015. - viii, 306 p. :ill., digital ;24 cm.

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrodinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.

ISBN: 9783319218731$q(electronic bk.)

Standard No.: 10.1007/978-3-319-21873-1doiSubjects--Topical Terms:

229270
Initial value problems.

LC Class. No.: QA378 / .R33 2015

Dewey Class. No.: 515.35

Lectures on nonlinear evolution equationsinitial value problems /
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100 1 $a Racke, Reinhard. $3 729249
245 1 0 $a Lectures on nonlinear evolution equations $h [electronic resource] : $b initial value problems / $c by Reinhard Racke.
250 $a 2nd ed.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2015.
300 $a viii, 306 p. : $b ill., digital ; $c 24 cm.
520 $a This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrodinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.
650 0 $a Initial value problems. $3 229270
650 0 $a Evolution equations, Nonlinear. $3 307743
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Partial Differential Equations. $3 274075
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