I've only learned differential equations for use in physics, and never took a rigorous math course on all their amazing features. So I'm hoping someone can teach me a bit here, in the context of this question:(adsbygoogle = window.adsbygoogle || []).push({});

Consider Maxwell's equations in vacuum, units don't matter here so I'll get rid of all constants:

[tex]\nabla \cdot \vec{E} = 0[/tex]

[tex]\nabla \cdot \vec{B} = 0[/tex]

[tex]\nabla \times \vec{E} = - \frac{\partial}{\partial t} \vec{B}[/tex]

[tex]\nabla \times \vec{B} = \frac{\partial}{\partial t} \vec{E}[/tex]

Now consider a finite region of space, with the boundary condition that the fields and their derivatives are zero on the boundary at time 0<=t<T. What solutions are there for the fields in the region during this time?

One obvious solution is: E=0, B=0 everywhere.

Is this question well posed enough to prove that this solution is unique?

If so, how? If not, what is missing?

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# How to prove uniqueness (or non-uniqueness) of solution

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