Mokhtar Kirane,
Salim Messaoudi
(2002)
We consider the systems of hyperbolic equations
⎧, t > 0, , (S1)
⎨
⎩, t > 0,
⎧, t > 0, , (S2)
⎨
⎩, t > 0, , (S3)
⎧, t > 0, ,
⎨
⎩, t > 0, ,
in with u(0,x) = u₀(x), v(0,x) = v₀(x), uₜ(0,x) = u₁(x), vₜ(0,x) = v₁(x). We show that, in each case, there exists a bound B on N such that for 1 ≤ N ≤ B solutions to the systems blow up in finite time.