Lectures on Nonlinear Evolution Equations

Initial Value Problems

Authors: Racke, Reinhard

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  • It serves since the first edition as a self-contained introduction into methods dealing with Cauchy problems for nonlinear evolutions equations presenting details for graduate students
  • Giving a survey for researchers in particular with an advanced topic on waveguides in the second edition
  • Only existing in separate original papers before
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eBook 79,72 €
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  • ISBN 978-3-319-21873-1
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Hardcover 103,99 €
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  • ISBN 978-3-319-21872-4
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Softcover 98,79 €
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  • ISBN 978-3-319-34259-7
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About this book

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 behaviour 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, Schrödinger 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.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook 79,72 €
price for Spain (gross)
  • ISBN 978-3-319-21873-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,99 €
price for Spain (gross)
  • ISBN 978-3-319-21872-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 98,79 €
price for Spain (gross)
  • ISBN 978-3-319-34259-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Nonlinear Evolution Equations
Book Subtitle
Initial Value Problems
Authors
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-21873-1
DOI
10.1007/978-3-319-21873-1
Hardcover ISBN
978-3-319-21872-4
Softcover ISBN
978-3-319-34259-7
Edition Number
2
Number of Pages
VIII, 306
Number of Illustrations
13 b/w illustrations
Additional Information
First edition published by Vieweg, Wiesbaden, 1992
Topics