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Math Help - Wave Equation - Maximum Principle

  1. #1
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    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!
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  2. #2
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    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.
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