Boundary Conditions and Data

  • Mass Per Pettersson
  • Gianluca Iaccarino
  • Jan Nordström
Part of the Mathematical Engineering book series (MATHENGIN)


We continue analysis of Burgers’ equation from the previous chapter with a focus on the effect of data for the boundary conditions. To facilitate understanding, we deal only with the truncated representation \(u(x,t,\xi ) = u_{0}\psi _{0} + u_{1}\psi _{1}\). This means that all the stochastic variation is accounted for by the single gPC coefficient u 1, and the standard deviation of the solution is simply | u 1 | . With this simplified setup, we obtain a few combinations of general situations for the boundary data: known expectation but unknown standard deviation, unknown expectation and standard deviation, etc. The implication in all these situations on well-posedness, stability and accuracy is discussed.


Unknown Standard Deviation Boundary Data Unknown Expectation Simple Apparatus Stochastic Variables 
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  1. 1.
    Pettersson P, Iaccarino G, Nordström J (2010) Boundary procedures for the time-dependent Burgers’ equation under uncertainty. Acta Math Sci 30(2):539–550. doi: 10.1016/S0252-9602(10)60061-6,

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mass Per Pettersson
    • 1
  • Gianluca Iaccarino
    • 2
  • Jan Nordström
    • 3
  1. 1.Uni ResearchBergenNorway
  2. 2.Department of Mechanical Engineering and Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  3. 3.Department of Mathematics Computational MathematicsLinköping UniversityLinköpingSweden

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