Energy Conservation in Wave Equations

This lecture covers the concept of energy conservation in wave equations, focusing on the uniqueness and existence of solutions. The instructor explains the Galerkin technique and the theory of systems of ordinary differential equations. The lecture also delves into the stability of solutions and the corresponding energy conservation. Through examples and exercises, students learn about the domain of dependence of solutions and the proof of D'Albert formula. The lecture concludes with discussions on energy conservation, initial conditions, and the span of solutions in wave equations.