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5. Fourth-Order Partial Differential Equations

  1. wtt + a2wxxxx = 0.    Equation of transverse vibration of elastic rods.
  2. wtt + a2wxxxx = Φ(x, t).    Equation of transverse vibration of elastic rods (nonhomogeneous).
  3. ΔΔw = 0.    Biharmonic equation.
  4. ΔΔw = Φ(x, y).    Nonhomogeneous biharmonic equation.

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