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How to prove uniqueness solution of the 3D wave

  1. Apr 19, 2013 #1
    1. The problem statement, all variables and given/known data

    The three dimensional wave equation:
    [itex]c∂^{2}u/∂t^2 = ∇^2 u[/itex]

    boundary conditions :
    [itex]u(x,y,z,t) = F(x,y,z,t)[/itex] on S

    initial conditions:
    [itex]u(x,y,z,0) = G(x,y,z)[/itex]

    [itex]∂u/∂t(x,y,z,0)=H(x,y,z)[/itex]

    2. Relevant equations
    how to prove the uniqueness solution of the above equation?

    3. The attempt at a solution
    Please recommend me some methods or examples to prove such problems. thansk
     
    Last edited: Apr 19, 2013
  2. jcsd
  3. Apr 19, 2013 #2

    mfb

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    For all x,y,z,t? If F is a given boundary condition, the unique solution u=F is trivial. If F is something else, or that condition is true for some x,y,z,t only, please specify this.

    Assuming u and u' are both solutions, what about u-u'?
     
  4. Apr 19, 2013 #3
    sorry! It's u(x,y,z,t) = F(x,y,z,t) on S
     
  5. Apr 20, 2013 #4

    mfb

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    Staff: Mentor

    Where is S?

    The initial conditions should be sufficient to get a unique solution.
     
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