A mechanism of smoothing due to evaporation condensation of the roughly perturbed surface of a solid is formulated as a Cauchy problem in the real line R1 for the equation ut =uxx/1 +ux2, which describes the evolution of the profile u(x,t) of the surface. In the preceding paper [A. Kitada and H. Umehara, J. Math. Phys. 28, 536 (1987)], it was demonstrated that, if the solution u(x,t) of the Cauchy problem is obtained in the classical sense with an additional restriction u∈C3(R1×(0,∞)), each peak in the surface decreases in height with time in the strict sense. In the present paper, by modifying the proof, it is shown that the additional restriction to the classical solution is excessive.

1.
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4.
The symbol Cm(Ω) denotes the set of all functions defined on Ω whose partial derivatives of order ⩽m are all continuous.
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6.
The partial derivative ∂F/∂q is abbreviated as Fq. In the same manner, we write ∂F/∂p as Fp.
7.
A.
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8.
Moreover, in the preceding paper,1 the extent of the generalization (P*) of the Mullins’ model was also limited by the excess restriction F∈C2(R2). In the present paper, this restriction is so softened as F∈C2(R2).
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© 1987 American Institute of Physics.
1987
American Institute of Physics