Nonlinear Differential Equations of Monotone Types in Banach Spaces

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9781441955418: Nonlinear Differential Equations of Monotone Types in Banach Spaces
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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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Recensione:

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 Moroşanu, 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)

Dalla quarta di copertina:

This book is concerned with basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type.

This is a monograph about the most significant results obtained in this area in last decades but is also written as a graduate textbook on modern methods in partial differential equations with main emphasis on applications to fundamental mathematical models of mathematical physics, fluid dynamics and mechanics.

This book is selfcontained while the prerequisites in functional analysis are necessary to understand as it is being presented in a preliminary chapter. An up-to-date list of references and extended comments are included.

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9781461425571: Nonlinear Differential Equations of Monotone Types in Banach Spaces

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ISBN 10:  1461425573 ISBN 13:  9781461425571
Casa editrice: Springer Verlag, 2012
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Descrizione libro Springer-Verlag New York Inc., United States, 2010. Hardback. Condizione: New. 2010 ed.. Language: English. Brand new Book. 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. Codice articolo APC9781441955418

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Descrizione libro Springer-Verlag New York Inc., United States, 2010. Hardback. Condizione: New. 2010 ed.. Language: English. Brand new Book. 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. Codice articolo APC9781441955418

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Descrizione libro Springer, 2010. Hardcover. Condizione: New. 2010. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. Buy with confidence, excellent customer service!. Codice articolo 1441955410n

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