Current equations describe everything pretty well but there are some issues considering inflation, quantum gravity, black holes,... How would we be able to verify that these do not evolve over long time periods, say several centuries? How would we describe someting like this? What would be the implications?
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We cannot prove that the laws of physics are unchanging over time, but we can set a good lower limit on how long it takes to change. Our current theories are capable of understanding what happens up to a very brief instant after the Big Bang, which indicates that if the laws of physics are changing, they're changing very slowly indeed.
Another thing to note is that, by Noether's Theorem, if the laws of physics are changing over time then energy will not be conserved, and vice versa. So as long as we observe energy conservation, we have indirect evidence that the laws of physics are not changing.
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