Stability of solutions to the Riemann problem for a thin film model of a perfectly soluble anti-surfactant solution

In this article, we consider a quasilinear hyperbolic system of partial differential equations governing the dynamics of a thin film of a perfectly soluble anti-surfactant liquid. We construct elementary waves of the corresponding Riemann problem and study their interactions. Further, we provide exact solution of the Riemann problem along with numerical examples. Finally, we show that the solution of the Riemann problem is stable under small perturbation of the initial data.

[1]  T. Sekhar,et al.  Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation , 2019, Communications on Pure & Applied Analysis.

[2]  T. Raja Sekhar,et al.  On the wave interactions in the drift-flux equations of two-phase flows , 2018, Appl. Math. Comput..

[3]  Yujin Liu,et al.  Wave Interactions and Stability of Riemann Solutions of the Aw–Rascle Model for Generalized Chaplygin Gas , 2018 .

[4]  T. Sekhar,et al.  Interaction of weak shocks in drift-flux model of compressible two-phase flows , 2018 .

[5]  K. Sefiane,et al.  Simple waves and shocks in a thin film of a perfectly soluble anti-surfactant solution , 2017 .

[6]  Minhajul,et al.  Elementary wave interactions in blood flow through artery , 2017 .

[7]  T. Raja Sekhar,et al.  Wave Interactions in Non-ideal Isentropic Magnetogasdynamics , 2017 .

[8]  V. Sharma,et al.  Wave interactions and stability of the Riemann solution for a strictly hyperbolic system of conservation laws , 2017 .

[9]  Yujin Liu,et al.  Elementary wave interactions in magnetogasdynamics , 2016 .

[10]  G. Sekhar,et al.  Thermocapillary migration of a spherical drop in an arbitrary transient Stokes flow , 2015 .

[11]  J. Snoeijer,et al.  Marangoni spreading due to a localized alcohol supply on a thin water film , 2013, 1312.6590.

[12]  Yanbo Hu,et al.  The Riemann problem of conservation laws in magnetogasdynamics , 2012 .

[13]  Renjun Duan,et al.  Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier-Stokes-Poisson equations , 2012 .

[14]  Sun Meina.  A note on the interactions of elementary waves for the AR traffic flow model without vacuum , 2011 .

[15]  Chun-fang Shen.  Wave interactions and stability of the Riemann solutions for the chromatography equations , 2010 .

[16]  T. Raja Sekhar,et al.  Riemann problem and elementary wave interactions in isentropic magnetogasdynamics , 2010 .

[17]  Meina Sun,et al.  Interactions of Elementary Waves for the Aw--Rascle Model , 2009, SIAM J. Appl. Math..

[18]  T. Raja Sekhar,et al.  Interaction of Shallow Water Waves , 2008 .

[19]  Zhibao Li,et al.  Surface tension of aqueous electrolyte solutions at high concentrations — representation and prediction , 2001 .

[20]  Michel Rascle,et al.  Resurrection of "Second Order" Models of Traffic Flow , 2000, SIAM J. Appl. Math..

[21]  A. Bressan.  Hyperbolic Systems of Conservation Laws , 1999 .

[22]  Sam Howison,et al.  A mathematical model for drying paint layers , 1997 .

[23]  P. Raviart,et al.  Numerical Approximation of Hyperbolic Systems of Conservation Laws , 1996, Applied Mathematical Sciences.

[24]  S. K. Wilson.  The levelling of paint films , 1993 .

[25]  W. S. Overdiep.  The levelling of paints , 1986 .

[26]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[27]  Tai-Ping Liu.  Quasilinear hyperbolic systems , 1979 .

[28]  F. Long,et al.  The Relative Surface Tension of Potassium Chloride Solutions by a Differential Bubble Pressure Method1 , 1942 .