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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.

Banach spaces. --- Banach-Raum. --- Differential equations, Nonlinear. --- Banach spaces --- Differential equations, Nonlinear --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Nonlinear differential equations --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Physics. --- Analysis. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Partial differential equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Nonlinear theories --- Functions of complex variables --- Generalized spaces --- Topology --- Global analysis (Mathematics). --- Differential equations, partial. --- Analysis, Global (Mathematics) --- Differential topology --- Geometry, Algebraic --- Mathematical physics. --- Physical mathematics --- Physics