The Resource Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models, by Marcelo R. Ebert, Michael Reissig, (electronic resource)
Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models, by Marcelo R. Ebert, Michael Reissig, (electronic resource)
Resource Information
The item Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models, by Marcelo R. Ebert, Michael Reissig, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models, by Marcelo R. Ebert, Michael Reissig, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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 CauchyKovalevskaja 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 nonstationary 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 nonlinearity of source and absorbing type in order to determine critical exponents: two wellknown 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 blowup behavior of local (in time) solutions. The last part features selected research projects and general background material.
 Language
 eng
 Extent
 1 online resource (XVI, 456 pages)
 Contents

 Part 1
 Introduction
 Part 2
 Partial differential equations in models
 Basics for partial differential equations
 The CauchyKovalevskaja 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
 Isbn
 9783319664569
 Label
 Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models
 Title
 Methods for Partial Differential Equations
 Title remainder
 Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models
 Statement of responsibility
 by Marcelo R. Ebert, Michael Reissig
 Language
 eng
 Summary
 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 CauchyKovalevskaja 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 nonstationary 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 nonlinearity of source and absorbing type in order to determine critical exponents: two wellknown 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 blowup behavior of local (in time) solutions. The last part features selected research projects and general background material.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Ebert, Marcelo R
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Reissig, Michael
 Series statement
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Partial differential equations
 Label
 Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models, by Marcelo R. Ebert, Michael Reissig, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Part 1  Introduction  Part 2  Partial differential equations in models  Basics for partial differential equations  The CauchyKovalevskaja 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
 Control code
 9783319664569
 Dimensions
 unknown
 Extent
 1 online resource (XVI, 456 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319664569
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319664569
 Other physical details
 1 illustration
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1026408145
 Label
 Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models, by Marcelo R. Ebert, Michael Reissig, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Part 1  Introduction  Part 2  Partial differential equations in models  Basics for partial differential equations  The CauchyKovalevskaja 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
 Control code
 9783319664569
 Dimensions
 unknown
 Extent
 1 online resource (XVI, 456 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319664569
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319664569
 Other physical details
 1 illustration
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1026408145
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/MethodsforPartialDifferentialEquations/xRxNciln2I/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/MethodsforPartialDifferentialEquations/xRxNciln2I/">Methods for Partial Differential Equations : Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models, by Marcelo R. Ebert, Michael Reissig, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>