A singularly perturbed problem related to surfactant spreading on thin films

Nonlinear Analysis, Theory, Methods and Applications

Volumn 27, Issue 3, 1996, Pages 287-296

  Renardy, Michael ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Continuous dependence; Hyperbolic parabolic systems; Shock structure; Singular perturbation; Surfactant driven flow

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; ITERATIVE METHODS; NAVIER STOKES EQUATIONS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; SURFACE ACTIVE AGENTS; THIN FILMS; VAN DER WAALS FORCES; VISCOSITY OF LIQUIDS;

ASYMPTOTIC SOLUTIONS; CONTINUOUS DEPENDENCE; COUETTE-POISEUILLE PROFILE; HYPERBOLIC PARABOLIC SYSTEMS; RANKINE HUGONIOT CONDITIONS; SHOCK STRUCTURE; SOBOLEV SPACE; SPATIAL DERIVATIVES; SURFACTANT DRIVEN FLOW;

EQUATIONS OF MOTION;

EID: 0030214525     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(95)00062-Z     Document Type: Article

References (6)

1. BORGAS M. S. & GROTBERG J. B., Monolayer flow on a thin film, J. Fluid Mech. 193, 151-170 (1988).
2. JENSEN O. E. & GROTBERG J. B., Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture, J. Fluid Mech. 240, 259-288 (1992).
3. JENSEN O. E., HALPERN D. & GROTBERG J. B., Surfactant-driven flows on thin viscous films: pulmonary drug delivery, in Surface-tension-driven Flows (Edited by G. P. NETTZEL and M. K. SMITH), AMD, Vol. 170. ASME, New York (1993).
4. RENARDY M., On an equation describing the spreading of surfactants on thin films, Nonlinear Analysis (to appear).
5. SMOLLER J., Shock Waves and Reaction-Diffusion Equations. Springer, New York (1983).
6. MICHELSON D., Steady solutions of the Kuramoto-Sivashinsky equation, Physica D 19, 89-111 (1986).