A.V. Babin's Books

Attractors of Evolution Equations

By: A.V. Babin,M.I. Vishik

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Attractors of Evolution Equations

By: A.V. Babin,M.I. Vishik

Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes system, which attracts (in an appropriate functional space) as t - ∞ all trajectories of this system, is a compact finite-dimensional (in the sense of Hausdorff) set. Upper and lower bounds (in terms of the Reynolds number) for the dimension of the attractor were found. These results for the Navier-Stokes system have stimulated investigations of attractors of other equations of mathematical physics. For certain problems, in particular for reaction-diffusion systems and nonlinear damped wave equations, mathematicians have established the existence of the attractors and their basic properties; furthermore, they proved that, as t - +∞, an infinite-dimensional dynamics described by these equations and systems uniformly approaches a finite-dimensional dynamics on the attractor U, which, in the case being considered, is the union of smooth manifolds. This book is devoted to these and several other topics related to the behaviour as t - ∞ of solutions for evolutionary equations.

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543

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Elsevier

Published Date

ISBN 10

0080875467

ISBN 13

9780080875460

Forest Insect Population Dynamics, Outbreaks, And Global Warming Effects

By: A. S. Isaev,Vladislav G. Soukhovolsky,O. V. Tarasova,E. N. Palnikova,A. V. Kovalev

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Forest Insect Population Dynamics, Outbreaks, And Global Warming Effects

By: A. S. Isaev,Vladislav G. Soukhovolsky,O. V. Tarasova,E. N. Palnikova,A. V. Kovalev

This new approach to insect modeling discusses population dynamics' regularities, control theory, theory of transitions, and describes methods of population dynamics and outbreaks modeling for forest phyllophagous insects and their effects on global climate change. Research in insect population dynamics is important for more reasons than just protecting forest communities. Insect populations are among the main ecological units included in the analysis of stability of ecological systems. Moreover, it is convenient to test new methods of analyzing population and community stability on the insect-related data, as by now ecologists and entomologists have accumulated large amounts of such data. In this book, the authors analyze population dynamics of quite a narrow group of insects – forest defoliators. It is hoped that the methods proposed herein for the analysis of population dynamics of these species may be useful and effective for analyzing population dynamics of other animal species and their effects and role in global warming. What can insects tell us about our environment and our ever-changing climate? It is through studies like this one that these important answers can be obtained, along with data on the insects and their behaviors themselves. The authors present new theories on modeling and data accumulation, using cutting-edge processes never before published for such a wide audience. This volume presents the state-of-the-art in the science, and it is an essential piece of any entomologist's and forest engineer's library.

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304

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John Wiley & Sons

Published Date

ISBN 10

1119407524

ISBN 13

9781119407522

Attractors of Evolution Equations

By: A.V. Babin,M.I. Vishik

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Attractors of Evolution Equations

By: A.V. Babin,M.I. Vishik

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

543

Publisher

Elsevier

Published Date

ISBN 10

0080875467

ISBN 13

9780080875460

Book's by A.V. Babin

Attractors of Evolution Equations

Attractors of Evolution Equations

Forest Insect Population Dynamics, Outbreaks, And Global Warming Effects

Forest Insect Population Dynamics, Outbreaks, And Global Warming Effects

Attractors of Evolution Equations

Attractors of Evolution Equations

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