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

Construction of solutions of a two‐dimensional Riemann problem for a thin film model of a perfectly soluble antisurfactant solution

“…For one-dimensional rotated solutions, we refer reader to previous works. 23,24 By comparing with the rotated one-dimensional solution in the succeeding sections, we verify that our constructed solution is globally unique.…”

“…which means that at any point on the discontinuity line, three of the characteristic lines, two corresponding to Γ 2 , and one to Γ 1 come into the point and the remaining one corresponding to Γ 1 goes out. We call the second kind of discontinuity a shock denoted by S, which satisfy ( 22) and the entropy conditions (23). It is easy to see that between any two states (h − , b − ) and (h + , b + ), the shock wave satisfies entropy condition if…”

“…$$ where $$$ h\left(x,t\right) $$$ is the dimensionless film thickness and $$$ b\left(x,t\right) $$$ denotes the bulk concentration gradient of solute. The above system was studied for classical wave interactions by Minhajul et al 23 and for nonclassical wave interactions by Sen and Raja Sekhar 24 . For more details on thin film flow and its modeling, we refer readers to previous works 18,25–29 and references cited therein.…”

Wave interactions in pressureless Cargo–LeRoux model with flux perturbation

“…Liu and Sun 17 described the interactions of the elementary waves for the one‐dimensional ideal magnetogasdynamics with transverse magnetic field by using characteristic analysis. Riemann problem and classical elementary wave interactions for various physical models have been studied in detail by Raja Sekhar et al 18–20 Sun 21 analyzed the wave interactions of elementary waves for traffic flow model. It can be found that the Riemann solutions are stable with respect to small perturbations of the initial data.…”

Optimal classification, exact solutions, and wave interactions of Euler system with large friction

“…Minhajul and Raja Sekhar discussed collision between weak discontinuity and elementary waves of Riemann problem for the multiphase flows. Stability of Riemann solutions for a thin film model of a perfectly soluble anti surfactant solution through wave interactions has been discussed by Minhajul et al Zeidan and Bira discussed the understanding and development of discontinuity waves and their structure in the context of polyatomic gases.…”