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Item Details
Title: ABSTRACT PARABOLIC EVOLUTION EQUATIONS AND THEIR APPLICATIONS
By: Atsushi Yagi
Format: Paperback

List price: £96.50


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ISBN 10: 3642261795
ISBN 13: 9783642261794
Publisher: SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG
Pub. date: 3 January, 2012
Edition: 2010 ed.
Series: Springer Monographs in Mathematics
Pages: 581
Description: This book offers an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations. It also shows how to apply the abstract results to various models in the real world focusing on various self-organization models.
Synopsis: This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0
Illustrations: 6 black & white illustrations, biography
Publication: Germany
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Returns: Returnable
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