Alexandre N. Carvalho's Books

Attractors Under Autonomous and Non-autonomous Perturbations

By: Matheus C. Bortolan,Alexandre N. Carvalho,José A. Langa

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Attractors Under Autonomous and Non-autonomous Perturbations

By: Matheus C. Bortolan,Alexandre N. Carvalho,José A. Langa

This book provides a comprehensive study of how attractors behave under perturbations for both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of non-autonomous dynamical systems is presented here for the first time in a unified manner. When modelling real world phenomena imprecisions are unavoidable. On the other hand, it is paramount that mathematical models reflect the modelled phenomenon, in spite of unimportant neglectable influences discounted by simplifications, small errors introduced by empirical laws or measurements, among others. The authors deal with this issue by investigating the permanence of dynamical structures and continuity properties of the attractor. This is done in both the autonomous (time independent) and non-autonomous (time dependent) framework in four distinct levels of approximation: the upper semicontinuity, lower semicontinuity, topological structural stability and geometrical structural stability. This book is aimed at graduate students and researchers interested in dissipative dynamical systems and stability theory, and requires only a basic background in metric spaces, functional analysis and, for the applications, techniques of ordinary and partial differential equations.

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Page Count

259

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470453088

ISBN 13

9781470453084

Attractors for infinite-dimensional non-autonomous dynamical systems

By: Alexandre Carvalho,José A. Langa,James Robinson

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Attractors for infinite-dimensional non-autonomous dynamical systems

By: Alexandre Carvalho,José A. Langa,James Robinson

The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.

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Page Count

434

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461445817

ISBN 13

9781461445814

One-Dimensional Turbulence and the Stochastic Burgers Equation

By: Alexandre Boritchev,Sergei Kuksin

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One-Dimensional Turbulence and the Stochastic Burgers Equation

By: Alexandre Boritchev,Sergei Kuksin

This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers equation with small viscosity under periodic boundary conditions and to interpreting the obtained results in terms of one-dimensional turbulence in a fictitious one-dimensional fluid described by the Burgers equation. The properties of one-dimensional turbulence which we rigorously derive are then compared with the heuristic Kolmogorov theory of hydrodynamical turbulence, known as the K41 theory. It is shown, in particular, that these properties imply natural one-dimensional analogues of three principal laws of the K41 theory: the size of the Kolmogorov inner scale, the 2/3 2/3-law, and the Kolmogorov–Obukhov law. The first part of the book deals with the stochastic Burgers equation, including the inviscid limit for the equation, its asymptotic in time behavior, and a theory of generalised L 1 L1-solutions. This section makes a self-consistent introduction to stochastic PDEs. The relative simplicity of the model allows us to present in a light form many of the main ideas from the general theory of this field. The second part, dedicated to the relation of one-dimensional turbulence with the K41 theory, could serve for a mathematical reader as a rigorous introduction to the literature on hydrodynamical turbulence, all of which is written on a physical level of rigor.

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Page Count

192

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470464365

ISBN 13

9781470464363

Attractors for infinite-dimensional non-autonomous dynamical systems

By: Alexandre Carvalho,José A. Langa,James Robinson

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Attractors for infinite-dimensional non-autonomous dynamical systems

By: Alexandre Carvalho,José A. Langa,James Robinson

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434

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461445809

ISBN 13

9781461445807

Book's by Alexandre N. Carvalho

Attractors Under Autonomous and Non-autonomous Perturbations

Attractors Under Autonomous and Non-autonomous Perturbations

Attractors for infinite-dimensional non-autonomous dynamical systems

Attractors for infinite-dimensional non-autonomous dynamical systems

One-Dimensional Turbulence and the Stochastic Burgers Equation

One-Dimensional Turbulence and the Stochastic Burgers Equation

Attractors for infinite-dimensional non-autonomous dynamical systems

Attractors for infinite-dimensional non-autonomous dynamical systems

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