All Partial Differential Equations Resources
Example Question #1 : Existence & Uniqueness
Determine if the statement is true or false:
The wave equation has at most one solution.
This statement is true by the Uniqueness Theorem.
is twice differential equation in terms of and .
Now, consider the energy integral
After performing integration by parts results in the following,
From here, the initial conditions and boundary conditions are applied.
which proves the wave equations has only one solution and thus is unique.