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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.
List of contents
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.
Summary
This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.
Additional text
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)
Report
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)
