Loading...
Publication
Existence and stability of regularized shock solutions, with applications to rimming flows
| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 468.88 KB | Adobe PDF |
Advisor(s)
Abstract(s)
This paper is concerned with regularization of shock solutions of nonlinear hyperbolic equations, i.e.,
introduction of a smoothing term with a coefficient ε, then taking the limit ε → 0. In addition to the classical use
of regularization for eliminating physically meaningless solutions which always occur in non-regularized equa tions (e.g. waves of depression in gas dynamics), we show that it is also helpful for stability analysis. The general
approach is illustrated by applying it to rimming flows, i.e., flows of a thin film of viscous liquid on the inside of a
horizontal rotating cylinder, with or without surface tension (which plays the role of the regularizing effect). In the
latter case, the spectrum of available linear eigenmodes appears to be continuous, but in the former, it is discrete and,
most importantly, remains discrete in the limit of infinitesimally weak surface tension. The regularized (discrete)
spectrum is fully determined by the point where the velocity of small perturbations vanishes, with the rest of the
domain, including the shock region, being unimportant.
Description
Keywords
Liquid films Rimming flows Shocks Stability Surface tension . Faculdade de Ciências Exatas e da Engenharia
Citation
Benilov, E. S., Benilov, M. S., & O’Brien, S. B. G. (2009). Existence and stability of regularized shock solutions, with applications to rimming flows. Journal of Engineering Mathematics, 63(2), 197-212. DOI: 10.1007/s10665-008-9227-1
Publisher
Springer