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Methods for Partial Differential Equations

Methods for Partial Differential Equations


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About the Book

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.


About the Author:

Marcelo Rempel Ebert (1977) is an Associate Professor at the Department of Computing and Mathematics at the University of São Paulo (USP). He obtained his Ph.D. degree in 2004 from Federal University of São Carlos, Brazil. His original contributions are mainly devoted to Evolution partial differential equations, in particular, questions related to the asymptotic behaviour and global existence of solutions for the Cauchy problem to semilinear wave equations.

Michael Gerhard Reissig (1958) is Professor for Partial Differential Equations at the Institute of Applied Analysis of the Technical University Bergakademie Freiberg. He obtained the degree Dr.rer.nat. in 1987, Dr.sc. in 1991 and Dr.habil. in 1992. His main contributions are devoted to the abstract Cauchy-Kovalevskaja theory, to Hele-Shaw flows, to elliptic equations, hyperbolic equations and Schrödinger equations as well.


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Product Details
  • ISBN-13: 9783319664552
  • Publisher: Birkhauser
  • Publisher Imprint: Birkhauser
  • Edition: 1st ed. 2018
  • Language: English
  • Returnable: Y
  • Sub Title: Qualitative Properties of Solutions, Phase Space Analysis, Semilinear Models
  • Width: 156 mm
  • ISBN-10: 3319664557
  • Publisher Date: 28 Mar 2018
  • Binding: Hardback
  • Height: 234 mm
  • No of Pages: 456
  • Spine Width: 27 mm
  • Weight: 924 gr


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