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Exact Solutions > Linear Partial Differential Equations > Second-Order Parabolic Partial Differential Equations

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1. Linear Parabolic Equations

  1. wt = awxx.    Heat equation (linear heat equation).
  2. wt = awxx + Φ(x, t).    Nonhomogeneous heat equation.
  3. wt = awxx + bwx + cw + Φ(x, t).    Convective heat equation with a source.
  4. wt = a(wrr + r−1wr).    Heat equation with axial symmetry.
  5. wt = a(wrr + r−1wr) + Φ(r, t).    Heat equation with axial symmetry (with a source).
  6. wt = a(wrr + 2r−1wr).    Heat equation with central symmetry.
  7. wt = a(wrr + 2r−1wr) + Φ(r, t).    Heat equation with central symmetry (with a source).
  8. iwt = −kwxx + U(x)w.    Schrodinger equation (linear Schrodinger equation).

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