An interface evolution problem for axisymmetric stressed pore channels

Abstract

The aim of this paper is the mathematical study of the time evolution of a stressed pore channel in an axisymmetric configuration. Under some conditions, morphological instabilities may appear at the material–vacuum interface. Assuming some formal asymptotic assumptions, we derive a nonlinear parabolic PDE (19) governing the cylindrical surface evolution. Local existence and unity of the solution of this PDE are shown and we also perform some numerical computations (with different parameters and initial condition), using a pseudo-spectral Galerkin method, yielding different behaviours for the solution to (19). In particular, we numerically observe what appears to be a finite time pinch-off.