Abstract
Consider a system of nonlinear wave equations for i=1,⋯,m, where Fi (i=1,⋯,m) are smooth functions of degree 2 near the origin of their arguments, and u=(u1,⋯,um), while ∂u and ∂x ∂u represent the first and second derivatives of u, respectively. In this paper, the author presents a new class of nonlinearity for which the global existence of small solutions is ensured. For example, global existence of small solutions for will be established, provided that .
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