Maximum Principle in Heat Equation

This lecture covers the application of the maximum principle in the context of the heat equation, focusing on the uniqueness theorem and the cylinder concept. The instructor explains the conditions under which the heat equation is satisfied and demonstrates the calculations involved. Through a series of examples and derivations, the lecture illustrates how the maximum principle can be used to analyze solutions to the heat equation and determine their behavior. The concept of the cylinder is introduced as a key element in understanding the properties of solutions. Various scenarios are explored to showcase the practical implications of the maximum principle in solving heat equation problems.