This book provides an accessible introduction to the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). Proceeding from a grounding in ordinary differential equations to attractors and inertial manifolds, the authors show how the basic theory of dynamical systems can be extended naturally and applied to study the asymptotic behavior of solutions of differential evolution equations. The material builds in a careful, gradual progression, developing the background needed by newcomers to the field and culminating in a more detailed presentation of the main topics than found in most sources.
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