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Lectures on nonlinear evolution equa...

Racke, Reinhard.

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Lectures on nonlinear evolution equations = initial value problems /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lectures on nonlinear evolution equations/ by Reinhard Racke.
其他題名:	initial value problems /
作者:	Racke, Reinhard.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	viii, 306 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Initial value problems. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-21873-1
ISBN:	9783319218731

Lectures on nonlinear evolution equations = initial 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

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

704464
Initial value problems.

LC Class. No.: QA378 / .R33 2015

Dewey Class. No.: 515.35

Lectures on nonlinear evolution equations = initial value problems /
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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.
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