Heat Equation: Basics and Stability Estimates

This lecture covers the basics of the heat equation, focusing on the diffusion of heat in different media. The instructor explains the heat equation, initial conditions, boundary conditions, and the importance of understanding the behavior of temperature over time. The lecture delves into the mathematical modeling of heat propagation, introducing Sobolev spaces for time-dependent problems. Stability estimates are discussed, showing how the solution's regularity is crucial for seeking discrete solutions. The instructor demonstrates the process of deriving stability estimates and emphasizes the significance of these estimates in proving the stability of solutions. The lecture concludes with details about the upcoming exam date.