Bounds of waiting-time in nonlinear diffusion Original Research Article

The solutions of the nonlinear diffusion equation ht = (hmhχ)χ may have a waiting-time, i.e., an initial finite time interval tω in which the front is at rest before starting to move. The theory gives us the value of tω only in a few special cases, when it is determined by the local behaviour near the front of the initial profile g(χ). However, in many instances tω depends on the global behaviour of g(χ), and in these cases the theory provides only upper and lower bounds that frequently may not be very helpful to estimate the tω. Here we discuss some global attributes that influence tω. Then we employ the values of tω obtained numerically for initial profiles of the power law type to obtain, for general initial profiles, bounds more stringent than those given by the current theory.