Prove that u(x, t) = sin |x| /|x| cost is a solution of the wave
equation utt − ∆u = 0 in R^3 . (Hint: use the formula for the
Laplacian of a function depending only on |x| in R^3 ). This
solution describes the spherical wave coming from infinity,
focusing at the origin, and bouncing back to infinity.
Prove that u(x, t) = sin |x| /|x| cost is a solution of the wave equation utt − ∆u = 0 in R^3 . (Hint: use the formula f
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Prove that u(x, t) = sin |x| /|x| cost is a solution of the wave equation utt − ∆u = 0 in R^3 . (Hint: use the formula f
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