Abstract
In this paper, we study the two-layered blood flow model within the framework of Lie symmetry analysis to investigate a range of closed-form solutions. Our investigation involves optimal classification, revealing the existence of six optimal subalgebras within the model. Further, we streamline the model by reducing it into a system of ordinary differential equations (ODEs), thereby deriving several exact solutions. Our analysis establishes the presence of the nonlinear self-adjointness property in the governing equation, leading to the development of various conservation laws. Furthermore, leveraging one of the exact solutions we obtained, we delve into the behaviour of characteristic shocks, C1 waves, and their interactions, providing a comprehensive understanding of their dynamics.
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