Ebook542 pages8 hours
Attractors of Evolution Equations
By A.V. Babin and M.I. Vishik
Rating: 0 out of 5 stars
()
About this ebook
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.
Related to Attractors of Evolution Equations
Titles in the series (23)
Mathematical Problems in Elasticity and Homogenization Rating: 0 out of 5 stars0 ratingsAsymptotic Analysis for Periodic Structures Rating: 0 out of 5 stars0 ratingsStochastic Control by Functional Analysis Methods Rating: 0 out of 5 stars0 ratingsThe Finite Element Method for Elliptic Problems Rating: 0 out of 5 stars0 ratingsMathematical Methods of Game and Economic Theory Rating: 2 out of 5 stars2/5Numerical Analysis of Variational Inequalities Rating: 0 out of 5 stars0 ratingsApplications of Variational Inequalities in Stochastic Control Rating: 2 out of 5 stars2/5Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems Rating: 0 out of 5 stars0 ratingsDifference Schemes: An Introduction to the Underlying Theory Rating: 0 out of 5 stars0 ratingsMathematical Models in Environmental Problems Rating: 0 out of 5 stars0 ratingsScattering Theory for Hyperbolic Operators Rating: 0 out of 5 stars0 ratingsSpectral Transform and Solitons Rating: 3 out of 5 stars3/5Introduction to the Theory of Linear Partial Differential Equations Rating: 0 out of 5 stars0 ratingsOperator Theory and Numerical Methods Rating: 0 out of 5 stars0 ratingsPseudo-Differential Operators on Manifolds with Singularities Rating: 0 out of 5 stars0 ratingsBoundary Value Problems in Mechanics of Nonhomogeneous Fluids Rating: 0 out of 5 stars0 ratingsSingular Perturbations I: Spaces and Singular Perturbations on Manifolds Without Boundary Rating: 0 out of 5 stars0 ratingsNonlinear Partial Differential Equations and Their Applications: College de France Seminar Volume XIV Rating: 0 out of 5 stars0 ratingsAttractors of Evolution Equations Rating: 0 out of 5 stars0 ratingsNumerical Analysis of Wavelet Methods Rating: 0 out of 5 stars0 ratingsReliable Methods for Computer Simulation: Error Control and Posteriori Estimates Rating: 0 out of 5 stars0 ratingsPatterns and Waves: Qualitative Analysis of Nonlinear Differential Equations Rating: 0 out of 5 stars0 ratings
Related ebooks
The Theory of Splines and Their Applications: Mathematics in Science and Engineering: A Series of Monographs and Textbooks, Vol. 38 Rating: 0 out of 5 stars0 ratingsStochastic Convergence Rating: 0 out of 5 stars0 ratingsIntroduction to the Mechanics of the Solar System Rating: 0 out of 5 stars0 ratingsAdvanced Theoretical Mechanics: A Course of Mathematics for Engineers and Scientists Rating: 0 out of 5 stars0 ratingsThe Theory of Splines and Their Applications Rating: 0 out of 5 stars0 ratingsIV: Analysis of Operators Rating: 4 out of 5 stars4/5Introduction to Singular Perturbations Rating: 0 out of 5 stars0 ratingsVolterra Integral and Differential Equations Rating: 0 out of 5 stars0 ratingsNonlinear Models of Interacting Populations Rating: 0 out of 5 stars0 ratingsScattering Theory for Hyperbolic Operators Rating: 0 out of 5 stars0 ratingsThe Application of Group Theory in Physics Rating: 0 out of 5 stars0 ratingsA Course of Mathematics for Engineers and Scientists: Theoretical Mechanics Rating: 0 out of 5 stars0 ratingsAdvances in Astronomy and Astrophysics Rating: 0 out of 5 stars0 ratingsBig-Planes, Boundaries and Function Algebras Rating: 0 out of 5 stars0 ratingsCollection of Problems in Classical Mechanics: International Series of Monographs in Natural Philosophy Rating: 3 out of 5 stars3/5Quantum Fluctuations Rating: 0 out of 5 stars0 ratingsSolutions In Action Rating: 0 out of 5 stars0 ratingsA Course of Mathematics for Engineers and Scientists: Volume 3: Theoretical Mechanics Rating: 1 out of 5 stars1/5Interpolation Functors and Interpolation Spaces Rating: 0 out of 5 stars0 ratingsWavelets: A Tutorial in Theory and Applications Rating: 0 out of 5 stars0 ratingsSingular Perturbations I: Spaces and Singular Perturbations on Manifolds Without Boundary Rating: 0 out of 5 stars0 ratingsMathematical Theory of Sedimentation Analysis: Physical Chemistry: A Series of Monographs Rating: 0 out of 5 stars0 ratingsNonmeasurable Sets and Functions Rating: 0 out of 5 stars0 ratingsCyclostratigraphy and the Milankovitch Theory Rating: 0 out of 5 stars0 ratingsDifferential Equations with Applications to Mathematical Physics Rating: 0 out of 5 stars0 ratingsMathematical Methods: Linear Algebra / Normed Spaces / Distributions / Integration Rating: 0 out of 5 stars0 ratingsVacuum Structure and QCD Sum Rules Rating: 0 out of 5 stars0 ratingsTransient Waves in Visco-Elastic Media Rating: 0 out of 5 stars0 ratingsOscillations in Nonlinear Systems Rating: 5 out of 5 stars5/5
Mathematics For You
Algebra - The Very Basics Rating: 5 out of 5 stars5/5Calculus For Dummies Rating: 4 out of 5 stars4/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5Geometry For Dummies Rating: 5 out of 5 stars5/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5Basic Math Notes Rating: 5 out of 5 stars5/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5The Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5Calculus Made Easy Rating: 4 out of 5 stars4/5See Ya Later Calculator: Simple Math Tricks You Can Do in Your Head Rating: 4 out of 5 stars4/5My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5A Mind for Numbers | Summary Rating: 4 out of 5 stars4/5GED® Math Test Tutor, 2nd Edition Rating: 0 out of 5 stars0 ratingsRelativity: The special and the general theory Rating: 5 out of 5 stars5/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsIs God a Mathematician? Rating: 4 out of 5 stars4/5The Elements of Euclid for the Use of Schools and Colleges (Illustrated) Rating: 0 out of 5 stars0 ratingsLogicomix: An epic search for truth Rating: 4 out of 5 stars4/5Algebra I For Dummies Rating: 4 out of 5 stars4/5
Reviews for Attractors of Evolution Equations
Rating: 0 out of 5 stars
0 ratings
0 ratings0 reviews
Book preview
Attractors of Evolution Equations - A.V. Babin
Enjoying the preview?
Page 1 of 1