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Blood circulation has fascinated minds since the Egyptians, but it was not until the eventeenth century and William Harvey to have a coherent view at the same time as a real revolution in medicine. After a brief history, a precise description of the heart, the motor of movement, seemed indispensable, followed by that of the multiple and varied vessels in which the blood flows and exchanges with the organs. This is followed by a fluid mechanics section and an incentive conclusion.
This paper makes a contribution by generalizing the classical series solution for initial boundary value problems of the one-dimensional reaction-diffusion equation on any finite interval of the real line. The general form of the equation is considered on a generic bounded interval and is subjected in the unified way to the three classical boundary conditions, namely the Neumann, Dirichlet, and Robin boundary conditions. The Fourier decomposition method, is used to derive the solution of the resulting homogeneous equation with zero boundary conditions. Subsequently, the solution of the nonhomogeneous equation with homogeneous boundary conditions is obtained using the Duhamel’s principle. Finally, the solution of the general problem is obtained as a convergent series over the considered interval, with the construction of an auxiliary. The Hopf-Cole transformation has facilitated the generalization of the exact solution of the Burger’s equation to generic intervals, as demonstrated by the described method.
