Narrow Results

The thin film equation is very important in electroanalytical chemistry arising in diffusion–reaction process. Considering the effort of the surface morphology on the diffusion process, the thin film equation is modified by using the fractal derivative, and its fractal variational principle is successfully established according to the semi-inverse method and two-scale transform method. It is very helpful to study the structure of the approximate solution.

In this paper we consider the thin film approximation of a 1D scalar conservation law with strictly convex flux. We prove that the sequence of approximate solutions converges to the unique Kružkov solution.

The authors study a generalized thin film equation. Under some assumptions on the initial value, the existence of weak solutions is established by the time-discrete method. The uniqueness and asymptotic behavior of solutions are also discussed.