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Partial Differential Equations

  • G. W. Bluman
  • J. D. Cole
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 13)

Abstract

The role of Lie theory in constructing solutions to partial differential equations differs essentially from its role for solving ordinary differential equations.(1) Invariance under a one-parameter Lie group of transformations reduces by one the number of variables appearing in a partial differential equation rather than the order as is the case for an ordinary differential equation. The method is not an encompassing as in Part 1 since it leads to particular (similarity) solutions and not to the “general” solution of a given partial differential equation. Thus boundary conditions play an important role in the applications of Lie theory to partial differential equations.

Keywords

Partial Differential Equation Fundamental Solution Heat Equation Dimensional Analysis Similarity Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1974

Authors and Affiliations

  • G. W. Bluman
    • 1
  • J. D. Cole
    • 2
  1. 1.Department of MathematicsThe University of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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