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Image of - Lectures on Nonlinerar Evolution Equations | 2nd Edition | Hardcover
Lectures on Nonlinerar Evolution Equations | 2nd Edition | Hardcover

Lectures on Nonlinerar Evolution Equations | 2nd Edition | Hardcover

by Racke

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided.In this second edition, initial-boundary value problems in waveguides are additionally considered.

Highlights

  • binding-icon

    9783319218724

    ISBN:

  • binding-icon

    Racke

    Author:

  • binding-icon

    306

    Pages:

  • binding-icon

    215 gm

    Weight:

  • langauage-icon

    English

    Language:

  • date-icon

    2015

    Year:

  • edition-icon

    2nd Edition

    Edition:

  • binding-icon

    Hardcover

    Binding:

₹8891

₹11114

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided.In this second edition, initial-boundary value problems in waveguides are additionally considered.

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