Lecture 5.4: Qualitative analysis of Wave equation - Uniqueness by Energy method
Channel: IIT Bombay July 2018
Date: 2021-09-18

In this lecture, a new time-dependent quantity called energy is associated to solution of the wave equation. By multiplying the wave equation with a suitable function and integrating by parts, it is proved that energy is a constant function. It is possible to prove uniqueness of solution of wave equation by conservation of energy. Conservation and dissipation of energy and uniqueness of solutions is demonstrated for variants of wave equation.