Let a be a constant ≠ -c. Find the solution u(x,t) of (4.1) in the quadrant
x > 0,1>0, for which
u=f(x), ut = g(x) for t =0, x > 0
ut=aux for x=0,t > 0,
where f and g are of class C² for x>0 and vanish near x=0. (Hint: Use (4.5)).
Show that generally no solution exists when α = - c.
Lu = utt - c²uᵪᵪ =0, (4.1)
u=F (x+ct)+G (x-ct). (4.5)
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