Forced Initial Boundary Value Problems for Burgers Equation

  • M. J. Ablowitz
  • S. De Lillo
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


In recent years there has been considerable research devoted towards the understanding of nonlinear evolution equations. There are a number of such equations which are exactly solvable and for which significant informations can be obtained. These studies are primarily directed towards autonomous equations with either rapidly decaying or periodic boundary values. On the other hand, forced nonlinear equations are certainly of physical significance. As such, the “forced” Burgers equation may be viewed as a prototypical model. In fact it describes the time evolution of onedimensional nonlinear diffusive systems under the influence of an external driver (see, for example, Ref. [1]).


Boundary Data Force Term Initial Boundary Burger Equation Dirac Delta Function 
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  1. [1]
    M. Kercher, G. Parisi and Y.C. Zheng, Physical Review Letters 56, 889 (1986).CrossRefADSGoogle Scholar
  2. [2]
    M.J. Ablowitz and S. De Lillo, “Forced and Semiline Solutions of Burgers Equation”, Preprint Program in Applied Mathematics, University of Colorado, Boulder, PAM #69, Jan 1991.Google Scholar
  3. [3]
    F. Calogero and S. De Lillo, Noralinearity 2, 37 (1989).CrossRefMATHADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • M. J. Ablowitz
    • 1
  • S. De Lillo
    • 2
  1. 1.Program in Applied MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Dipartimento di FisicaUniversità di Perugia, and I.N.F.N. Sezione di PerugiaPerugiaItaly

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