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The present paper is devoted to finding conditions on the occurrence of scattering for strictly hyperbolic systems with time‐dependent coefficients whose time‐derivatives are in  L  1  in time. More precisely, it will be shown that the solutions are asymptotically free if the coefficients are stable in the sense that their improper Riemann integrals converge as  t  → ±∞, while each nontrivial solution with radially symmetric data is never asymptotically free provided that the coefficients are not stable as  t  → ±∞. As a by‐product, wave and scattering operators can be constructed. An important feature is that assumptions on only one derivative of the coefficients are made so that the results would be applicable to the asymptotic behaviour of Kirchhoff systems.

Scattering for strictly hyperbolic systems with time‐dependent coefficients