  We study two initial value problems of the linear diffusion equation and a
nonlinear diffusion equation, when Cauchy data are bounded and oscillate
mildly. The latter nonlinear heat equation is the equation of the curvature
flow, when the moving curves are represented by graphs. By using an elementary
scaling technique, we show some formulas for space-time behavior of the
solution.
  Keywords: scaling argument, self-similar solution, nonstabilizing solution,
nontrivial dynamics, nontrivial large-time behavior, irregular behavior.
