Viorel Barbu

Nonlinear Differential Equations of Monotone Types in Banach Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

In the last decades, functional methods played an increasing role in the qualita tive theory of partial differential equations. The spectral methods and theory of C 0 semigroups of linear operators as well as Leray-Schauder degree theory, ?xed point theorems, and theory of maximal monotone nonlinear operators are now essential functional tools for the treatment of linear and nonlinear boundary value problems associated with partial differential equations. An important step was the extension in the early seventies of the nonlinear dy namics of accretive (dissipative) type of the Hille-Yosida theory of C semigroups 0 of linear continuous operators. The main achievement was that the Cauchy problem associated with nonlinear m accretive operators in Banach spaces is well posed and the corresponding dynamic is expressed by the Peano exponential formula from ?nite dimensional theory. This fundamental result is the corner stone of the whole existence theory of nonlinear in?nite dynamics of dissipative type and its contri bution to the development of the modern theory of nonlinear partial differential equations cannot be underestimated.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 272
• Erscheinungstermin: 1. Januar 2010
• Englisch
• ISBN-13: 9781441955425
• Artikelnr.: 37349694

Inhaltsangabe

Fundamental Functional Analysis.- Maximal Monotone Operators in Banach Spaces.- Accretive Nonlinear Operators in Banach Spaces.- The Cauchy Problem in Banach Spaces.- Existence Theory of Nonlinear Dissipative Dynamics.

Rezensionen

From the reviews:

"This book presents the main results concerning monotone and accretive operators as well as a lot of applications associated with such operators. ... It is worth pointing out that the book relies on the author's long experience in research and teaching at different universities. ... The book is useful for both graduate students and researchers." (Gheorghe Morosanu, Zentralblatt MATH, Vol. 1197, 2010)

"The present treatise completes it, by putting the emphasis upon the application of maximal monotone and accretive nonlinear operators in a Banach space to nonlinear dissipative dynamics, and in particular to the study of some time-dependent nonlinear partial differential equations seen as evolution equations in Banach spaces. ... Each chapter ends with bibliographical remarks and a list of references, and thus ... an excellent guide to the present literature, recommended as well to graduate students as to experts in the area." (Jean Mawhin, Mathematical Reviews, Issue 2011 d)

"The book is well written, with many details, and is very understandable. ... this is a significant book on the subject of nonlinear semigroups that most nonlinear analysts should have on their shelves." (Nicholas D. Alikakos, SIAM Review, Vol. 53 (3), 2011)