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Asymptotic behavior of classical solutions to a system of semilinear wave equations in low space dimensions. (English) Zbl 1016.35050
The authors give a new a priori estimate for a classical solution of the nonhomogeneous wave equation in $$\mathbb{R}^n\times \mathbb{R},$$ where $$n=2,3.$$ Under some conditions on $$p, q,$$ they construct a global solution of the system $$u_{tt}-\triangle u=|v|^p$$, $$v_{tt}-\triangle v=|u|^q,$$ which is asymptotic to a pair of solutions to a homogeneous wave equation with small initial data.

##### MSC:
 35L70 Second-order nonlinear hyperbolic equations 35B45 A priori estimates in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35B33 Critical exponents in context of PDEs
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