Solution of the Diffusion Equation in Free Space
摘要
In this chapter, we focus on solving the diffusion equation under no spatial constraints, that is, in free space, to find a unique solution that will satisfy both the partial differential equation and the initial condition. To such end, we will review the most widely used: the Fourier and Laplace transforms and the Green’s function formalism, presenting the complete step-by-step process for each. We also discuss the implications and consequences of the central limit theorem, which is a mainstay of statistics and probability.