Exponential Asymptotics for Thin Film Rupture

• Autores: S. Jonathan Chapman, Philippe H. Trinh, Thomas P. Witelski
• Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 1, 2013, págs. 232-253
• Idioma: inglés
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• Resumen

  • The formation of singularities in models of many physical systems can be described using self-similar solutions. One particular example is the finite-time rupture of a thin film of viscous fluid which coats a solid substrate. Previous studies have suggested the existence of a discrete, countably infinite number of distinct solutions of the nonlinear differential equation which describes the self-similar behavior. However, no analytical mechanism for determining these solutions was identified. In this paper, we use techniques in exponential asymptotics to construct the analytical selection condition for the infinite sequence of similarity solutions, confirming the conjectures of earlier numerical studies.