Blow-up of solutions of some nonlinear hyperbolic systems
K Deng - The Rocky Mountain Journal of Mathematics, 1999 - JSTOR
The Rocky Mountain Journal of Mathematics, 1999•JSTOR
We consider two hyperbolic systems: utt= Δu+| v| p, vtt= Δv+| u| q and utt= Δu+| vt| p, vtt= Δv+|
ut| q in Rn×(0,∞) with u (x, 0)= f (x), v (x, 0)= h (x), ut (x, 0)= g (x), vt (x, 0)= k (x). We show that
there exists a bound B (n, p) such that if 1< pq< B (n, p) all nontrivial solutions with compact
support blow up in finite time.
ut| q in Rn×(0,∞) with u (x, 0)= f (x), v (x, 0)= h (x), ut (x, 0)= g (x), vt (x, 0)= k (x). We show that
there exists a bound B (n, p) such that if 1< pq< B (n, p) all nontrivial solutions with compact
support blow up in finite time.
We consider two hyperbolic systems: utt = Δu + |v|p, vtt = Δv + |u|q and utt = Δu + |vt|p, vtt = Δv + |ut|q in Rn × (0, ∞) with u(x, 0) = f(x), v(x, 0) = h(x), ut(x, 0) = g(x), vt(x, 0) = k(x). We show that there exists a bound B(n, p) such that if 1 < pq < B(n, p) all nontrivial solutions with compact support blow up in finite time.
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