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Methods for Partial Differential Equations: Qualitative Properties of
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eBay-Artikelnr.:277499669591
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- MPN
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- ISBN
- 9783319664552
Über dieses Produkt
Product Identifiers
Publisher
Springer International Publishing A&G
ISBN-10
3319664557
ISBN-13
9783319664552
eBay Product ID (ePID)
240571093
Product Key Features
Number of Pages
Xvi, 456 Pages
Publication Name
Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models
Language
English
Publication Year
2018
Subject
Differential Equations / General, Differential Equations / Partial
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Weight
32.1 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Reviews
"This is a self-contained monograph on the theory of partial differential equations, mainly oriented for nonlinear hyperbolic and dispersive equations and systems. ... This monograph is totally a good introduction to the beginners of the study of partial differential equations, particularly to whom are interested in wave and dispersive equations and systems." (Takashi Suzuki, zbMATH 1503.35003, 2023) "This book contains both a careful presentation of several important theoretic notions and properties but also a selection of well-chosen exercises at the end of each chapter. ... The exposition is flexible enough to allow substantial changes in the presentation of the arguments without compromising comprehension ... . this volume is a valuable resource for advanced undergraduate and graduate students ... . This book may also be useful for Ph.D. students or for special courses or seminars." (Vicentiu D. Radulescu, Mathematical Reviews, October, 2018), "This book contains both a careful presentation of several important theoretic notions and properties but also a selection of well-chosen exercises at the end of each chapter. ... The exposition is flexible enough to allow substantial changes in the presentation of the arguments without compromising comprehension ... . this volume is a valuable resource for advanced undergraduate and graduate students ... . This book may also be useful for Ph.D. students or for special courses or seminars." (Vicentiu D. Radulescu, Mathematical Reviews, October, 2018)
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
Part 1.- Introduction.- Part 2.- Partial differential equations in models.- Basics for partial differential equations.- The Cauchy-Kovalevskaja theorem.- Holmgren's uniqueness theorem.- Method of characteristics.- Burger's equation.- Laplace equation - properties of solutions - starting point of elliptic theory.- Heat equation - properties of solutions - starting point of parabolic theory.- Wave equation - properties of solutions - starting point of hyperbolic theory.- Energies of solutions - one of the most important quantities.- Part 3.- Phase space analysis for heat equation.- Phase space analysis and smoothing for Schrödinger equations.- Phase space analysis for wave models.- Phase space analysis for plate models.- The method of stationary phase and applications.- Part 4.- Semilinear heat models.- Semilinear classical damped wave models.- Semilinear wave models with a special structural dissipation.- Semilinear classical wave models.- Semilinear Schrödinger models.- Linear hyperbolic systems.- Part 5.- Research projects for beginners.- Background material.
Synopsis
This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the "research project for beginners" proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible toprove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material., Provides an overview on different topics of the theory of partial differential equations Presents a comprehensive treatment of semilinear models by using appropriate qualitative properties and a-priori estimates of solutions to the corresponding linear models and several methods to treat non-linearities Supports the preparation of courses on selected topics of the theory of partial differential equations for advanced undergraduate and graduate students, This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the "research project for beginners" proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.
LC Classification Number
QA370-380
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- m***m (339)- Bewertung vom Käufer.Letzter MonatBestätigter KaufBest shipping excellent packaging. Great price item was as described.
- a***t (159)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufPackage well packed shipping was fast the lazer and flashlight worked as described well worth the money Good ebayer!TYSEAM USB Rechargeable 800 Lumens Green Laser Gun Light Flashlight. (Nr. 277123880740)
- p***p (249)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufSuper Fast Shipping! Packaged perfectly so it didn’t get any damage during shipping. Exactly as described! Price is very comparable to others. Great Product!OSMO Pocket 3 Hard Case Multifunctional Portable Waterproof for DJI (Nr. 276652510814)