How to prove uniqueness solution of the 3D wave

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Homework Statement



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

boundary conditions :
u(x,y,z,t) = F(x,y,z,t) on S

initial conditions:
u(x,y,z,0) = G(x,y,z)

∂u/∂t(x,y,z,0)=H(x,y,z)

Homework Equations


how to prove the uniqueness solution of the above equation?

The Attempt at a Solution


Please recommend me some methods or examples to prove such problems. thansk
 
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boundary conditions :
u(x,y,z,t)=F(x,y,z,t)
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'?
 
sorry! It's u(x,y,z,t) = F(x,y,z,t) on S
 
Where is S?

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