The Resource A stability technique for evolution partial differential equations : a dynamical systems approach, Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)

A stability technique for evolution partial differential equations : a dynamical systems approach, Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)

Label
A stability technique for evolution partial differential equations : a dynamical systems approach
Title
A stability technique for evolution partial differential equations
Title remainder
a dynamical systems approach
Statement of responsibility
Victor A. Galaktionov, Juan Luis Vázquez
Creator
Contributor
Subject
Genre
Language
eng
Summary
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
Member of
Action
digitized
Cataloging source
OCLCE
http://library.link/vocab/creatorName
Galaktionov, Victor A
Dewey number
515/.353
Illustrations
illustrations
Index
index present
LC call number
QA377
LC item number
.G223 2004
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Vazquez, J. L.
Series statement
Progress in nonlinear differential equations and their applications
Series volume
v. 56
http://library.link/vocab/subjectName
  • Differential equations, Partial
  • Differential equations, Parabolic
  • Differentiable dynamical systems
  • Stability
  • Équations aux dérivées partielles
  • Équations différentielles paraboliques
  • Dynamique différentiable
  • Stabilité
  • Partielle Differentialgleichung
  • Parabolische Differentialgleichung
  • Differenzierbares dynamisches System
  • Équations aux dérivées partielles
  • Dynamique différentiable
  • Stabilité
  • Differentiable dynamical systems
  • Differential equations, Parabolic
  • Differential equations, Partial
  • Stability
Label
A stability technique for evolution partial differential equations : a dynamical systems approach, Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4612-2050-3
Instantiates
Publication
Antecedent source
file reproduced from original
Bibliography note
Includes bibliographical references (p. [359]-374) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction: A Stability Approach and Nonlinear Models -- Stability Theorem: A Dynamical Systems Approach -- Nonlinear Heat Equations: Basic Models and Mathematical Techniques -- Equation of Superslow Diffusion -- Quasilinear Heat Equations with Absorption. The Critical Exponent -- Porous Medium Equation with Critical Strong Absorption -- The Fast Diffusion Equation with Critical Exponent -- The Porous Medium Equation in an Exterior Domain -- Blow-up Free-Boundary Patterns for the Navier-Stokes Equations -- The Equation ut = uxx + uln2u: Regional Blow-up -- Blow-up in Quasilinear Heat Equations Described by Hamilton-Jacobi Equations -- A Fully Nonlinear Equation from Detonation Theory -- Further Applications to Second- and Higher-Order Equations -- References -- Index
Dimensions
24 cm.
Dimensions
unknown
Extent
xix, 377 p.
Form of item
online
Isbn
9781461220503
Isbn Type
(electronic bk.)
Level of compression
  • lossless
  • lossy
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4612-2050-3
Other physical details
ill.
Reformatting quality
  • preservation
  • access
Reproduction note
Electronic reproduction.
Specific material designation
remote
System control number
  • (OCoLC)872631822
  • (OCoLC)ocn872631822
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Label
A stability technique for evolution partial differential equations : a dynamical systems approach, Victor A. Galaktionov, Juan Luis Vázquez, (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4612-2050-3
Publication
Antecedent source
file reproduced from original
Bibliography note
Includes bibliographical references (p. [359]-374) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
black and white
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction: A Stability Approach and Nonlinear Models -- Stability Theorem: A Dynamical Systems Approach -- Nonlinear Heat Equations: Basic Models and Mathematical Techniques -- Equation of Superslow Diffusion -- Quasilinear Heat Equations with Absorption. The Critical Exponent -- Porous Medium Equation with Critical Strong Absorption -- The Fast Diffusion Equation with Critical Exponent -- The Porous Medium Equation in an Exterior Domain -- Blow-up Free-Boundary Patterns for the Navier-Stokes Equations -- The Equation ut = uxx + uln2u: Regional Blow-up -- Blow-up in Quasilinear Heat Equations Described by Hamilton-Jacobi Equations -- A Fully Nonlinear Equation from Detonation Theory -- Further Applications to Second- and Higher-Order Equations -- References -- Index
Dimensions
24 cm.
Dimensions
unknown
Extent
xix, 377 p.
Form of item
online
Isbn
9781461220503
Isbn Type
(electronic bk.)
Level of compression
  • lossless
  • lossy
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4612-2050-3
Other physical details
ill.
Reformatting quality
  • preservation
  • access
Reproduction note
Electronic reproduction.
Specific material designation
remote
System control number
  • (OCoLC)872631822
  • (OCoLC)ocn872631822
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

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