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A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach Softcover Repri Edition
Contributor(s): Galaktionov, Victor A. (Author), Vázquez, Juan Luis (Author)

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 ISBN: 146127396X     ISBN-13: 9781461273967
Publisher: Birkhauser
OUR PRICE: $52.24  

Binding Type: Paperback - See All Available Formats & Editions
Published: February 2012
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Click for more in this series: Progress in Nonlinear Differential Equations and Their Appli
Additional Information
BISAC Categories:
- Mathematics | Differential Equations - Partial
- Technology & Engineering | Mechanical
- Mathematics | Mathematical Analysis
Dewey: 515.353
Series: Progress in Nonlinear Differential Equations and Their Appli
Physical Information: 0.82" H x 6.14" W x 9.21" L (1.23 lbs) 377 pages
Features: Bibliography
 
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Publisher Description:
common feature is that these evolution problems can be formulated as asymptoti- cally small perturbations of certain dynamical systems with better-known behaviour. Now, it usually happens that the perturbation is small in a very weak sense, hence the difficulty (or impossibility) of applying more classical techniques. Though the method originated with the analysis of critical behaviour for evolu- tion PDEs, in its abstract formulation it deals with a nonautonomous abstract differ- ential equation (NDE) (1) Ut = A(u) ] C(u, t), t > 0, where u has values in a Banach space, like an LP space, A is an autonomous (time-independent) operator and C is an asymptotically small perturbation, so that C(u(t), t) as t 00 along orbits {u(t)} of the evolution in a sense to be made precise, which in practice can be quite weak. We work in a situation in which the autonomous (limit) differential equation (ADE) Ut = A(u) (2) has a well-known asymptotic behaviour, and we want to prove that for large times the orbits of the original evolution problem converge to a certain class of limits of the autonomous equation. More precisely, we want to prove that the orbits of (NDE) are attracted by a certain limit set 2* of (ADE), which may consist of equilibria of the autonomous equation, or it can be a more complicated object.
 
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