A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach (Progress in Nonlinear Differential Equations and Their Applications)

Book Description

This book introduces a new, state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations; much of the text is dedicated to the application of this method to a wide class of nonlinear diffusion equations. The underlying theory hinges on a new stability result, formulated in the abstract setting of infinite-dimensional dynamical systems, which states that under certain hypotheses, the omega-limit set of a perturbed dynamical system is stable under arbitrary asymptotically small perturbations.

The Stability Theorem is examined in detail in the first chapter, followed by a review of basic results and methods---many original to the authors---for the solution of nonlinear diffusion equations. Further chapters provide a self-contained analysis of specific equations, with carefully-constructed theorems, proofs, and references. In addition to the derivation of interesting limiting behaviors, the book features a variety of estimation techniques for solutions of semi- and quasilinear parabolic equations.

Written by established mathematicians at the forefront of the field, this work is a blend of delicate analysis and broad application, appropriate for graduate students and researchers in physics and mathematics who have basic knowledge of PDEs, ordinary differential equations, functional analysis, and some prior acquaintance with evolution equations. It is ideal for a course or seminar in evolution equations and asymptotics, and the book's comprehensive index and bibliography will make it useful as a reference volume as well.

Analytic Semigroups and Optimal Regularity in Parabolic Problems (Progress in Nonlinear Differential Equations and Their Applications)

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Analytic Semigroups and Optimal Regularity in Parabolic Problems (Progress in Nonlinear Differential Equations and Their Applications)
Alessandra Lunardi
Manufacturer: Birkhäuser Basel
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Binding: Hardcover

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ASIN: 3764351721

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The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems.
Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones.
Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived.
The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques.

Evolution Equations Semigroups and Functional Analysis: In Memory of Brunello Terreni (Progress in Nonlinear Differential Equations and Their Applications)

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Evolution Equations Semigroups and Functional Analysis: In Memory of Brunello Terreni (Progress in Nonlinear Differential Equations and Their Applications)

Manufacturer: Birkhäuser Basel
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Binding: Hardcover

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ASIN: 3764367911

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Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics: EVEQ2000 Conference in Levico Terme (Trento, Italy), October 30 - ... Equations and Their Applications)

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Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics: EVEQ2000 Conference in Levico Terme (Trento, Italy), October 30 - ... Equations and Their Applications)

Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover

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ASIN: 3764303743

Book Description

The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.

Among the recent advances treated are new developments in

- moving boundary problems

- asymptotics in non-linear Volterra equations

- Poincaré inequality on stratified sets

- behaviour of granular matter

- stochastic aspects of the Hamilton-Jacobi-Bellmann equation

- very general Paley-Wiener results applied to both classical and generalized functions

- Ornstein-Uhlenbeck operators

- semigroup approach in economics (pricing theory)

- convolution-evolution equation in aeroelasticity

Local Jet Bundle Formulation of Bäcklund Transformations: With Applications to Nonlinear Evolution Equations (Mathematical Physics Studies)

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Local Jet Bundle Formulation of Bäcklund Transformations: With Applications to Nonlinear Evolution Equations (Mathematical Physics Studies)
F.A.E. Pirani , D.C. Robinson , and W.F. Shadwick
Manufacturer: Springer
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Binding: Paperback

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Nonlinear Evolution Equations and Applications (Mathematics and its Applications)

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Nonlinear Evolution Equations and Applications (Mathematics and its Applications)
Gheorghe Morosanu
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 9027724865

Nonlinear Evolution Equations and Their Applications: Proceedings of the Luso-Chinese Symposium Macau 7-9 October 1998

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Nonlinear Evolution Equations and Their Applications: Proceedings of the Luso-Chinese Symposium Macau 7-9 October 1998

Manufacturer: World Scientific Publishing Company
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Nonlinear Evolution Equations that Change Type (The IMA Volumes in Mathematics and its Applications)

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Nonlinear Evolution Equations that Change Type (The IMA Volumes in Mathematics and its Applications)

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 0387973532

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This volume will be of interest to applied mathematicians, to researchers in Partial Differential Equations, and to those involved in Fluid Dynamics and Numerical Analysis examining models for viscoelastic flows, porous medium and granular flows, and flows exhibiting phase transitions. As papers in this volume indicate, physical processes whose simplest models may involve change of type occur also in other dynamic contexts, such as in the simulation of oil reservoirs, involving multiphase flow in a porous medium, and in granular flow.

Nonlinear Stochastic Evolution Problems in Applied Sciences (Mathematics and Its Applications)

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Nonlinear Stochastic Evolution Problems in Applied Sciences (Mathematics and Its Applications)
N. Bellomo , Z. Brzezniak , and L.M. de Socio
Manufacturer: Springer
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Binding: Hardcover

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Book Description

This volume deals with the analysis of nonlinear evolution problems described by partial differential equations having random or stochastic parameters. The emphasis throughout is on the actual determination of solutions, rather than on proving the existence of solutions, although mathematical proofs are given when this is necessary from an applications point of view. The content is divided into six chapters.
Chapter 1 gives a general presentation of mathematical models in continuum mechanics and a description of the way in which problems are formulated. Chapter 2 deals with the problem of the evolution of an unconstrained system having random space-dependent initial conditions, but which is governed by a deterministic evolution equation. Chapter 3 deals with the initial-boundary value problem for equations with random initial and boundary conditions as well as with random parameters where the randomness is modelled by stochastic separable processes. Chapter 4 is devoted to the initial-boundary value problem for models with additional noise, which obey Ito-type partial differential equations. Chapter 5 is essential devoted to the qualitative and quantitative analysis of the chaotic behaviour of systems in continuum physics. Chapter 6 provides indications on the solution of ill-posed and inverse problems of stochastic type and suggests guidelines for future research. The volume concludes with an Appendix which gives a brief presentation of the theory of stochastic processes.
Examples, applications and case studies are given throughout the book and range from those involving simple stochasticity to stochastic illposed problems.
For applied mathematicians, engineers and physicists whose work involves solving stochastic problems.

Qualitative Aspects And Applications of Nonlinear Evolution Equations

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Qualitative Aspects And Applications of Nonlinear Evolution Equations
H. Beirao Da Veiga
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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The well-known works of literature in this series constitute the most valuable treasures of universal literature. The affordably priced imitation leather bound books enhance any library, putting the works of Dante, Dumas, Hugo, and Tolstoy within everyone's reach.

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Ana Karenina
Leon Tolstoi
Manufacturer: ALBA
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Binding: Hardcover
ASIN: B000Q9U0TG

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Ana Karenina
Leon Tolstoi
Manufacturer: Editorial Porrua
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ASIN: B000KZ46QE

Ana Karenina (Obras Selectas de Leon Tolstoi)

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Ana Karenina (Obras Selectas de Leon Tolstoi)

Manufacturer: Editorial del Valle de Mexico
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ASIN: B000BYEGGE

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Ana Karenina - 2 Tomos
Leo Tolstoy
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Ana Karenina 2 Vols

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Analisis De Ana Karenina
Alfonso Carvajal
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Ana Karenina

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ASIN: 968890418X

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Ana Karenina 1
Leon Tolstoi
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Ana Karenina 2
Leon Tolstoi
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