Functional Methods in Differential Equations - Brossura

Hokkanen, Veli-Matti; Morosanu, Gheorghe

Brossura

ISBN 10: 1584882832 ISBN 13: 9781584882831

Casa editrice: Chapman and Hall/CRC, 2002

Riassunto

In recent years, functional methods have become central to the study of theoretical and applied mathematical problems. As demonstrated in this Research Note, functional methods can not only provide more generality, but they can also unify results and techniques and lead to better results than those obtained by classical methods. Presenting entirely original results, the authors use functional methods to explore a broad range of elliptic, parabolic, and hyperbolic boundary value problems and various classes of abstract differential and integral equations. They show that while it is crucial to choose an appropriate functional framework, this approach can lead to mathematical models that better describe concrete physical phenomena. In particular, they reach a concordance between the physical sense and the mathematical sense for the solutions of some special models. Beyond its importance as a survey of the primary techniques used in the area, the results illuminated in this volume will prove valuable in a wealth of interesting applications Readership: This volume will be of interest to pure and applied mathematicians, engineers, and physicists.

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Contenuti

INTRODUCTION
Function and Distribution Spaces
Monotone Operators, Convex Functions, and Subdifferentials
Some Elements of Spectral Theory
Linear Evolution Equations and Semigroups
Nonlinear Evolution Equations
ELLIPTIC BOUNDARY VALUE PROBLEMS
Non-Degenerate Elliptic Boundary Value Problems
Degenerate Elliptic Boundary Value Problems
PARABOLIC BOUNDARY VALUE PROBLEMS WITH ALGEBRAIC BOUNDARY CONDITIONS
Homogeneous Boundary Conditions
Nonhomogeneous Boundary Conditions
Higher Regularity of Solutions
PARABOLIC BOUNDARY VALUE PROBLEMS WITH ALGEBRAIC-DIFFERENTIAL BOUNDARY CONDITIONS
Homogeneous Boundary Conditions
Nonhomogeneous Boundary Conditions
Higher Regularity of Solutions
HYPERBOLIC BOUNDARY VALUE PROBLEMS WITH ALGEBRAIC BOUNDARY CONDITIONS
Existence, Uniqueness and Long-Time Behavior of Solutions
Higher Regularity of Solutions
HYPERBOLIC BOUNDARY VALUE PROBLEMS WITH ALGEBRAIC-DIFFERENTIAL BOUNDARY CONDITIONS
Existence, Uniqueness and Long-Time Behavior of Solutions
Higher Regularity of Solutions
THE FOURIER METHOD FOR ABSTRACT DIFFERENTIAL EQUATIONS
First Order Linear Equations
Semilinear First Order Equations
Second Order Linear Equations
Semilinear Second Order Equations
THE SEMIGROUP APPROACH FOR ABSTRACT DIFFERENTIAL EQUATIONS
Semilinear Fist Order Equations
Hyperbolic Partial Differential Systems with Nonlinear Boundary Conditions
NONLINEAR NON-AUTONOMOUS ABSTRACT DIFFERENTIAL EQUATIONS
First Order Differential and Functional Equations Containing Subdifferentials
An Application
IMPLICIT NONLINEAR ABSTRACT DIFFERENTIAL EQUATIONS
Existence of Solution
Uniqueness of Solution
Continuous Dependence of Solution
Existence of Periodic Solutions

Dettagli dell'edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 1584882832
• ISBN 13: 9781584882831
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 264
• Contatto del produttore: non disponibile
• Persona responsabile: Buchpark GmbH; gpsr@buchpark.de; ; Krügerweg 1; Trebbin; Brandenburg; 14959; Germania