Diffusion Equations: Green's Function Approach

This lecture focuses on the analysis of diffusion equations using Green's function approach. The instructor discusses the limitations of traditional methods, such as sine and cosine expansion, and introduces the concept of finding a solution to partial differential equations (PDE) with boundary conditions (BC). The lecture emphasizes the importance of dimensional analysis, particularly in the context of diffusion length scales. The instructor presents similarity solutions and their formulation, demonstrating how to derive solutions for specific boundary conditions. The discussion includes the application of initial conditions and the significance of normalized distributions. The lecture also covers the construction of general solutions using linearity and homogeneity principles, providing a comprehensive understanding of how to solve diffusion equations effectively. Throughout the lecture, various mathematical expressions and equations are presented to illustrate the concepts discussed, ensuring a clear and structured approach to the topic.