Benjamin-Bona-Mahony Equation on Finite Trees
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The aim of this thesis is to explore the use of a system of Benjamin-Bona-Mahony (BBM) equations with dissipation to represent a pressure wave through a finite tree. Such systems arise as crude models of arterial blood flow. We show that there exists a unique solution for the coupled system of equations representing the pressure wave on a single junction for a positive interval and that this solution is regular. We also show that the coupled system of equations is a solution to the original system of BBM equations. Subsequently, we expand this analysis to a finite tree. Additionally, we present numerical simulations of the pressure wave for different scenarios. We find that aspects of the numerically simulated solution correlate with those of pressure waves in contextual situations.
coupled system of equations