Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations

Volume 7

V. Lakshmikantham, S. Koksal

328 pages, parution le 14/03/2003

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Résumé

This volume describes the monotone iterative technique which is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This when combined with the quasilinearization method offers rapid convergence of approximation to the solution and this has played a valuable role in unifying a variety of nonlinear problems.

The monograph is divided into two parts. The first part describes the general methodology systematically utilizing the classic approach and the second part exhibits the development of the same basic ideas via the variational technique. The volumes provides a useful and timely reference text for applied scientists, engineers and numerical analysts.

Contents

Elliptic Equations

Introduction
Monotone Iterates: A Preview
Monotone Iterative Technique
Generalized Quasilinearization
Weakly Coupled Mixed Monotone Systems
Elliptic Systems in Unbounded Domains
MIT Systems in Unbounded Domains
Notes and Comments
Parabolic Equations
Introduction
Comparison Theorems
Monotone Iterative Technique
Generalized Quasilinearization
Monotone Flows and Mixed Monotone Systems
GCR for Weakly Coupled Systems
Stability and Vector Lyapunov Functions
Notes and Comments
Impulsive Parabolic Equations
Introduction
Comparison Results for IPS
Coupled Lower and Upper Solutions
Generalized Quasilinearization
Population Dynamics with Impulses
Notes and Comments
Hyperbolic Equations
Introduction
VP and Comparison Results
Monotone Iterative Technique
The Method of Generalized Quasilinearization
Notes and Comments
Elliptic Equations
Introduction
Comparison Result
MIT: Semilinear Problems
MIT: Quasilinear Problems
MIT: Degenerate Problems
GQ: Semilinear Problems
GQ: Quasilinear Problem
GQ: Degenerate Problems
Notes and Comments
Parabolic Equations
Introduction
Monotone Iterative Technique
Generalized Quasilinearization
Nonlocal Problems
GQ: Nonlocal Problems
Quasilinear Problems
GQ: Quasilinear Problems
Notes and Comments
Hyperbolic Equations
Introduction
Notation and Comparison Results
Monotone Iterative Technique
Generalized Quasilinearization
Notes and Comments
Appendices
Sobolev Spaces
Elliptic Equations
Parabolic Equations
Impulsive Differential Equations
Hyperbolic Equations

Caractéristiques techniques

	PAPIER
Éditeur(s)	Taylor and Francis Books
Auteur(s)	V. Lakshmikantham, S. Koksal
Parution	14/03/2003
Nb. de pages	328
Format	17,8 x 25,2
Couverture	Relié
Poids	720g
Intérieur	Noir et Blanc
EAN13	9780415305280
ISBN13	978-0-415-30528-0