Uniqueness of the solution with certain boundary conditions

AI Thread Summary
The discussion revolves around the uniqueness of solutions in electrodynamics when applying Dirichlet or Neumann boundary conditions. It highlights that the uniqueness of solutions can depend on the specific equations being solved and the nature of the boundary conditions. Linear equations typically guarantee a unique solution under these conditions, prompting a suggestion to prove this mathematically. Participants emphasize the importance of understanding the characteristics of the equations involved. The conversation ultimately seeks clarity on the mathematical foundations of these principles in electrodynamics.
M. next
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Hey!


Speaking electrodynamics, I can't seem to get mathematically or even physically convinced that the solution with Dirichlet or Neumann boundary conditions is UNIQUE.

Can someone explain it?

Thanks.
 
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What equation are you solving? Sometimes you have uniqueness, sometimes you might not depending on the problem and the boundary conditions.
 
M. next said:
Hey!


Speaking electrodynamics, I can't seem to get mathematically or even physically convinced that the solution with Dirichlet or Neumann boundary conditions is UNIQUE.

Can someone explain it?

Thanks.
Are the equations linear? If so, are you aware that the solution has to be unique? See if you can prove this mathematically by making use of the characteristics of linear equations.

Chet
 
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