Sur un problème d'évolution d'interface dans le cas axisymétrique

The paper is concerned with a surface evolution problem in the cylindrical case. The physical configuration consists in an axisymmetric stressed pore channel as described in [J. Colin, J. Grilhé, N. Junqua, Morphological instabilities of a stressed pore channel, Acta Mater. 45 (9) (1997) 3835-3841]. When axial stress is applied, morphological instabilities may appear at the vacuum/material interface. Under the axial symmetry envisaged, the radius r(z,τ) of the pore channel satisfies a nonlinear evolution equation. Under some formal asymptotic assumptions as in [M. Boutat, Y. D'Angelo, S. Hilout, V. Lods, Existence and finite-time blow-up for the solution to a thin-film surface evolution problem, Asymptotic Anal. 38 (2) (2004) 93-128], we obtain a parabolic 4th-order PDE. Local existence and uniqueness of the solution is established and numerical results showing either a dissipative behaviour or a pinch-off of the solution (depending on initial condition and value of the parameter η) are obtained. To cite this article: M. Boutat et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).