The Energy Method: Uniqueness of Solutions to ODEs and PDEs

An ordinary differential equation (ODE) is an equation involving a scalar-valued function from the real line to the real line, and some of its derivatives. A partial differential equation (PDE) is a generalization of the ordinary differential equation to the event where the argument is in multiple dimensions. In this case we have partial derivatives in each direction. For example, if the input is an ordered pair, then the input belongs to R², so we may have partial derivatives in two different directions. No matter if we’re dealing with an ODE or a PDE…