TWO-DIMENSIONAL NON-SELF-SIMILAR RIEMANN SOLUTIONS FOR A THIN FILM MODEL OF A PERFECTLY SOLUBLE ANTI-SURFACTANT SOLUTION

In this article, we construct non-self-similar Riemann solutions for a twodimensional quasilinear hyperbolic system of conservation laws which describes the fluid flow in a thin film for a perfectly soluble anti-surfactant solution. The initial Riemann data consists of two different constant states separated by a smooth curve in x ??? y plane, so without using self-similarity transformation and dimension reduction, we establish solutions for five different cases. Further, we consider interaction of all possible nonlinear waves by taking initial discontinuity curve as a parabola to develop the structure of global entropy solutions explicitly.