Two-dimensional non-self-similar Riemann solutions for a thin film model of a perfectly soluble anti-surfactant solution

Barthwal, Rahul; Raja Sekhar, T.

doi:10.1090/qam/1625

Authors: Rahul Barthwal and T. Raja Sekhar
Journal: Quart. Appl. Math. 80 (2022), 717-738
MSC (2020): Primary 35L65, 35L40; Secondary 35L67, 35L03, 74K35
DOI: https://doi.org/10.1090/qam/1625
Published electronically: May 26, 2022
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Abstract: In this article, we construct non-self-similar Riemann solutions for a two-dimensional 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.

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