# Math Help - Wave Equation - Maximum Principle

1. ## Wave Equation - Maximum Principle

I have come across the following question:

Does the wave equation have a maximum principle? Either state such a maximum principle or justify your answer with a counterexample.

I am sure that the wave equation has no maximum principle and it is intuitively obvious as the wave equation just moves information along the characteristic lines, but I cannot come up with an explicit example that works!

Any help you could offer would be much appreciated!

2. How do you define a maximum principle for a PDE? For example an identical form of the strong maximum principle for the heat equation (in bounded domains) clearly can't work: Take boundary conditions and intial velocity 0 and take any $f\geq 0$ (as initial contition) that assumes a maximum inside the domain.