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Attractors For Degenerate Parabolic Type Equations

Attractors for Degenerate Parabolic Type Equations PDF
Author: Messoud Efendiev
Publisher: American Mathematical Soc.
ISBN: 1470409852
Size: 37.97 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 221
View: 398

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Attractors For Degenerate Parabolic Type Equations

by Messoud Efendiev, Attractors For Degenerate Parabolic Type Equations Books available in PDF, EPUB, Mobi Format. Download Attractors For Degenerate Parabolic Type Equations books, This book deals with the long-time behavior of solutions of degenerate parabolic dissipative equations arising in the study of biological, ecological, and physical problems. Examples include porous media equations, -Laplacian and doubly nonlinear equations, as well as degenerate diffusion equations with chemotaxis and ODE-PDE coupling systems. For the first time, the long-time dynamics of various classes of degenerate parabolic equations, both semilinear and quasilinear, are systematically studied in terms of their global and exponential attractors. The long-time behavior of many dissipative systems generated by evolution equations of mathematical physics can be described in terms of global attractors. In the case of dissipative PDEs in bounded domains, this attractor usually has finite Hausdorff and fractal dimension. Hence, if the global attractor exists, its defining property guarantees that the dynamical system reduced to the attractor contains all of the nontrivial dynamics of the original system. Moreover, the reduced phase space is really "thinner" than the initial phase space. However, in contrast to nondegenerate parabolic type equations, for a quite large class of degenerate parabolic type equations, their global attractors can have infinite fractal dimension. The main goal of the present book is to give a detailed and systematic study of the well-posedness and the dynamics of the semigroup associated to important degenerate parabolic equations in terms of their global and exponential attractors. Fundamental topics include existence of attractors, convergence of the dynamics and the rate of convergence, as well as the determination of the fractal dimension and the Kolmogorov entropy of corresponding attractors. The analysis and results in this book show that there are new effects related to the attractor of such degenerate equations that cannot be observed in the case of nondegenerate equations in bounded domains. This book is published in cooperation with Real Sociedad Matemática Española (RSME).




Recent Trends In Dynamical Systems

Recent Trends in Dynamical Systems PDF
Author: Andreas Johann
Publisher: Springer Science & Business Media
ISBN: 3034804512
Size: 18.33 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 616
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Recent Trends In Dynamical Systems

by Andreas Johann, Recent Trends In Dynamical Systems Books available in PDF, EPUB, Mobi Format. Download Recent Trends In Dynamical Systems books, This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.




Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations

Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations PDF
Author: Messoud Efendiev
Publisher: Springer
ISBN: 3319984071
Size: 53.18 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 258
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Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations

by Messoud Efendiev, Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations Books available in PDF, EPUB, Mobi Format. Download Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations books, This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.




Galois Theories Of Linear Difference Equations An Introduction

Galois Theories of Linear Difference Equations  An Introduction PDF
Author: Charlotte Hardouin
Publisher: American Mathematical Soc.
ISBN: 1470426552
Size: 80.96 MB
Format: PDF, ePub
Category : Difference and functional equations -- Difference equations -- Linear equations
Languages : en
Pages : 171
View: 168

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Galois Theories Of Linear Difference Equations An Introduction

by Charlotte Hardouin, Galois Theories Of Linear Difference Equations An Introduction Books available in PDF, EPUB, Mobi Format. Download Galois Theories Of Linear Difference Equations An Introduction books, This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.




The Octagonal Pets

The Octagonal PETs PDF
Author: Richard Evan Schwartz
Publisher: American Mathematical Soc.
ISBN: 1470415224
Size: 31.20 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 212
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The Octagonal Pets

by Richard Evan Schwartz, The Octagonal Pets Books available in PDF, EPUB, Mobi Format. Download The Octagonal Pets books, A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmüller theory. This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semi-regular octagons. The 1-parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semi-regular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computer-assisted calculations.




Handbook Of Differential Equations Evolutionary Equations

Handbook of Differential Equations  Evolutionary Equations PDF
Author: C.M. Dafermos
Publisher: Elsevier
ISBN: 9780080931975
Size: 37.66 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 608
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Handbook Of Differential Equations Evolutionary Equations

by C.M. Dafermos, Handbook Of Differential Equations Evolutionary Equations Books available in PDF, EPUB, Mobi Format. Download Handbook Of Differential Equations Evolutionary Equations books, The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area - Continuation of previous volumes in the handbook series covering Evolutionary PDEs - Written by leading experts




Mathematical Reviews

Mathematical Reviews PDF
Author:
Publisher:
ISBN:
Size: 76.15 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages :
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Mathematical Reviews

by , Mathematical Reviews Books available in PDF, EPUB, Mobi Format. Download Mathematical Reviews books,




Differential Equations

Differential Equations PDF
Author: Angelo Favini
Publisher: CRC Press
ISBN: 9781420011135
Size: 47.99 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 304
View: 4531

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Differential Equations

by Angelo Favini, Differential Equations Books available in PDF, EPUB, Mobi Format. Download Differential Equations books, With contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exciting possibilities not only in the future of mathematics but also in physics, engineering, superconductivity in special materials, and other scientific fields. Exploring the hypotheses and numerical approaches that relate to pure and applied mathematics, this collection of research papers and surveys extends the theories and methods of differential equations. The book begins with discussions on Banach spaces, linear and nonlinear theory of semigroups, integrodifferential equations, the physical interpretation of general Wentzell boundary conditions, and unconditional martingale difference (UMD) spaces. It then proceeds to deal with models in superconductivity, hyperbolic partial differential equations (PDEs), blowup of solutions, reaction-diffusion equation with memory, and Navier-Stokes equations. The volume concludes with analyses on Fourier-Laplace multipliers, gradient estimates for Dirichlet parabolic problems, a nonlinear system of PDEs, and the complex Ginzburg-Landau equation. By combining direct and inverse problems into one book, this compilation is a useful reference for those working in the world of pure or applied mathematics.




Referativny Zhurnal

Referativny   zhurnal PDF
Author:
Publisher:
ISBN:
Size: 77.30 MB
Format: PDF
Category : Mathematics
Languages : ru
Pages :
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Referativny Zhurnal

by , Referativny Zhurnal Books available in PDF, EPUB, Mobi Format. Download Referativny Zhurnal books,