| Abstract: |
| We consider the Cauchy problem for a weakly coupled system of semilinear damped wave equations in \(\mathbb{R}^N\) (\(N=1,2,3\)). We prove the global existence of mild solutions for sufficiently small initial data and derive weighted pointwise space-time decay estimates. These estimates provide a refined description of the decay of each component in time and space. In particular, depending on the nonlinearity exponent relative to the Fujita critical exponent, the solutions exhibit different decay patterns, including an asymmetric regime in which one component decays more slowly and a logarithmic correction in the borderline case. The proof is based on weighted \(L^\infty\)-estimates for the linear damped wave equation. |
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