A moving boundary problem describing the growth of a droplet in its vapour

Vito Antonio Cimmelli (1) , Francesco Dell'Isola (2, 3)

1 DMI - Dipartimento di Matematica e Informatica
2 Dipartimento di Ingegneria Strutturale e Geotecnica
3 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita

In [1-5] and [12] the theory of shells is generalized: nonmaterial bidimensional continua are introduced in order to model capillarity phenomena. In this paper we solve some mathematical problems arising when the quoted models are used to describe the growth in its vapour of a sufficiently small drop in the neighbourhood of an equilibrium state. We start to consider the source terms appearing in the integro-differential parabolic evolution equations (IDE) deduced in [5] for the temperature field in the vapour phase. We prove that, due to coupling between the capillarity and thermomechanical phenomena occuring close to the interface, these terms have both space and time Holder coefficients equal to that one relative to the second time-derivative of the radius of the droplet. To our knowledge only Gevrey [14] partially treated this case for PDE of parabolic type. We improve his results in order to prove the well-posedness of the moving boundary problem formulated in [5] for IDE.

Domains: Mechanics [physics.med-ph]

Vito Antonio Cimmelli, Francesco Dell'Isola. A moving boundary problem describing the growth of a droplet in its vapour. Archives of Mechanics, 1993, pp.20. ⟨hal-00502282⟩