Dynamics of Multilayer Shear Flows

Igor L. Kliakhandler ()
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Igor L. Kliakhandler: Michigan Technological University, Department of Mathematical Sciences

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2003, pp 645-654 from Springer

Abstract: Abstract The multi-layer shear flows are one of the most graphic and experimentally accessible examples of conservation laws system. The flows are interesting due to their conceptual simplicity, rich dynamical phenomenology, and technological relevance. The simplest system is multilayer thin film flowing down an inclined plane the process used in manufacturing of color photographic films and papers. Conservation of mass in each layer leads to a system of coupled PDEs. Its hyperbolic part corresponds to a kinematic part of the motion. Investigation of its structure reveals a very nontrivial types of behaviour that might appear in such system. Namely, in addition to hyperbolic waves, the system may also exhibit elliptic behaviour. The influence of dissipative effects results in a simple and remarkable manifestation of the result obtained by Majda and Pego (1985): that the dissipative terms may in fact destabilize the hyperbolic system, and that the solutions of viscosity-smoothed system do not converge to the solutions of the corresponding hyperbolic system.

Keywords: Surface Tension; Hyperbolic System; Incline Plane; Complex Eigenvalue; Multilayer Thin Film (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55711-8_60

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DOI: 10.1007/978-3-642-55711-8_60

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