EAN: 9783110549256

INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS VOLUME 1...

This two-volume work presents state-of-the-art mathematical theories and results on
infinite-dimensional dynamical systems. Inertial manifolds  approximate inertial manifolds 
discrete attractors and the dynamics of small dissipation are discussed in detail. The unique
combination of mathematical rigor and physical background makes this work an essential
reference for researchers and graduate students in applied mathematics and physics. The main
emphasis in the first volume is on the mathematical analysis of attractors and inertial
manifolds. This volume deals with the existence of global attractors  inertial manifolds and
with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution
equations in modern physics. Known as well as many new results about the existence  regularity
and properties of inertial manifolds and approximate inertial manifolds are also presented in
the first volume. The second volume will be devoted to modern analytical tools and methods in
infinite-dimensional dynamical systems. ContentsAttractor and its dimension estimationInertial
manifoldThe approximate inertial manifold

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