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Dynamics of evolutionary equations. (English) Zbl 1254.37002
Applied Mathematical Sciences 143. New York, NY: Springer (ISBN 0-387-98347-3/hbk). xiii, 670 p. (2002).
Publisher’s description: The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations which attempt to model phenomena that change with time, and the infinite dimensional aspects occur when forces that describe the motion depend on spatial variables. This book may serve as an entree for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations. It begins with a brief essay on the evolution of evolutionary equations and introduces the origins of the basic elements of dynamical systems, flow and semiflow.
Table of contents: Preface. 1. The evolution of evolutionary systems. 2. Dynamical systems: basic theory. 3. Linear semigroups. 4. Basic theory of evolutionary equations. 5. Nonlinear partial differential equations. 6. Navier Stokes dynamics. 7. Basic principles of dynamics. 8. Inertial manifolds and the reduction principle. Appendices: Basics of functional analysis.

MSC:
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
37Lxx Infinite-dimensional dissipative dynamical systems
34G20 Nonlinear differential equations in abstract spaces
35K55 Nonlinear parabolic equations
35L70 Second-order nonlinear hyperbolic equations
35Q30 Navier-Stokes equations
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