Galpern—Sobolev Type Equations with Non-constant Coefficients

  • K. Gürlebeck
  • W. Sprößig
Part of the Trends in Mathematics book series (TM)


We study Galpern—Sobolev equations by the help of a quaternionic operator calculus. Some previous work will be extended to the case of variable coefficients. Rothe’s time discretization method is used to reduce the problem to a series of stationary problems. Solving the resulting stationary problems by means of quaternionic analysis we obtain integral representation formulas for the solution of the Galpern-Sobolev equation. The truncation error and the stability of the method is studied, too.


Galpern—Sobolev equations representation formulas operator calculus finite difference schemes 

Mathematics Subject Classification (2000)

Primary: 30G35 Secondary 35G15 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • K. Gürlebeck
    • 1
  • W. Sprößig
    • 2
  1. 1.Bauhaus-University WeimarWeimarGermany
  2. 2.TU Bergakademie Freiberg, Fakultät für Mathematik und InformatikFreibergGermany

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