Second-Order Linear Parabolic Equations

  • Joel Smoller
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 258)


Parabolic equations arise in diffusion processes, and more generally in “irreversible” time-dependent processes. Mathematically, this is reflected in the fact that the equations are not invariant under the reversal of time ; i.e., under the transformation t → —t. This means that knowledge about the “past” is lost as time increases. For example, there may be dissipation effects which lead to an increase in entropy and a consequent loss of information.


Line Segment Parabolic Equation Heat Equation Auxiliary Function Horizontal Segment 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Joel Smoller
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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