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Monographs in Mathematics

Linear and Quasilinear Parabolic Problems

Volume I: Abstract Linear Theory

Authors: Amann, Herbert

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About this book

In this treatise we present the semigroup approach to quasilinear evolution equa­ of parabolic type that has been developed over the last ten years, approxi­ tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic­ ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille­ Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-0348-9221-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-3-7643-5114-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $139.99
price for USA in USD
  • ISBN 978-3-0348-9950-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Linear and Quasilinear Parabolic Problems
Book Subtitle
Volume I: Abstract Linear Theory
Authors
Series Title
Monographs in Mathematics
Series Volume
89
Copyright
1995
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Verlag Basel
eBook ISBN
978-3-0348-9221-6
DOI
10.1007/978-3-0348-9221-6
Hardcover ISBN
978-3-7643-5114-4
Softcover ISBN
978-3-0348-9950-5
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XXXV, 338
Topics