Nonlinear Differential Equations of Monotone Types in Banach Spaces (Springer Monographs in Mathematics Book 0)

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. Front Matter....Pages I-X Fundamental Functional Analysis....Pages 1-26 Maximal Monotone Operators in Banach Spaces....Pages 27-96 Accretive Nonlinear Operators in Banach Spaces....Pages 97-126 The Cauchy Problem in Banach Spaces....Pages 127-192 Existence Theory of Nonlinear Dissipative Dynamics....Pages 193-270 Back Matter....Pages 271-272 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.