Abstract
In this paper we will prove that the positive initial-energy solution for coupled nonlinear Klein-Gordon equations with degenerate damping and source terms grows exponentially.
Highlights
[13] Rammaha and Sakuntasathien focus on the global well-posedness of the system of nonlinear wave equation (1.6)
They prove a global nonexistence for certain solutions with positive initial energy, the main tool proof is a method used in [15]
H (t − s) ∆v (x, s) ds + |vt|q−1 vt = f2 (u, v). Is unbounded and it grows up as an exponential fonction as time goes to infinity, provided that the initail data are large enough
Summary
In [13] Rammaha and Sakuntasathien focus on the global well-posedness of the system of nonlinear wave equation (1.6). [11] Erhen Piskin prove the blow up of solutions of (1.1) in finite time with negative initial energy and nondegenerate damping terms. They prove a global nonexistence for certain solutions with positive initial energy, the main tool proof is a method used in [15] . [9] There exist two positive constants c1 and c2 such that c1 |u|2(r+2) + |v|2(r+2) ≤ 2 (r + 2) F (u, v) ≤ c2 |u|2(r+2) + |v|2(r+2) , (2.5)
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