Affiliations: Laboratoire de Mathématiques, Université de Poitiers, Boulevard Marie et Pierre Curie, Téléport 2, BP 30179, 86962 Futuroscope Chasseneuil cedex, France E-mails: [email protected], [email protected] | CORIA-INSA, UMR 6614 CNRS, Université de Rouen, 76801 St-Etienne du Rouvray, France E-mail: [email protected] | Département de Mathématiques Appliquées et Informatique, Faculté des Sciences et Techniques, BP 523, 23000 Béni-Mellal, Maroc E-mail: [email protected]
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.
Keywords: nonlinear partial differential equations, finite time pinch-off, initial boundary value problem, local solution
