Functional methods in differential equations

著者

• Hokkanen, Veli-Matti
• Moroșanu, Gheorghe

書誌事項

Functional methods in differential equations

Veli-Matti Hokkanen, Gheorghe Moroșanu

（Research notes in mathematics, 432）

Chapman & Hall/CRC, c2002

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

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

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詳細情報

• NII書誌ID(NCID): BA57367326
• ISBN:
  • 1584882832
• LCCN: 2002018853
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Boca Raton, Fla.
• ページ数/冊数: xiii, 243 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA379
  • DC21 : 515/.35
• 件名:
  • LCSH : Boundary value problems
  • LCSH : Functional analysis
• 親書誌ID:
  • BA41222266