Two exact viscous and nonsteady solutions of Burgers' nonlinear diffusion equation are derived which show how sawtooth discontinuities or dissipation layers broaden and decay. One solution is in the ``physical space''; the other is a discrete spatial Fourier series. Spectral coefficients of the second solution satisfy (exactly) an infinite set of coupled nonlinear ordinary differential equations. Energetics of the two solutions are briefly discussed.
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Edward R. Benton (1967) studied this question.
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