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Three of these four describe the one-dimensional heat equation. The exception is

  • A.it needs an initial temperature distribution as well as boundary conditions
  • B.disturbances travel along characteristics at a finite speed
  • C.it is parabolic
  • D.its solutions become smoother as time advances

Answer: B

Finite-speed propagation along characteristics belongs to the hyperbolic wave equation. The classical heat equation is parabolic, its solutions smooth with time, and it does require both an initial distribution and conditions at the ends. Its disturbances spread instantly in principle, which is a known shortcoming of the model

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