Asymptotics for symmetric hyperbolic systems with a large parameter

The asymptotic behavior as λ → ∞ is analysed for solutions u(λ) of quasilinear symmetric hyperbolic systems of the form A0ut + Ajuxi + λCjuxj = Fu(0, x, λ) = u0(x, λ), where the Ak and F depend on t, x, u, and uλ, but the Cj are constant. The results are applied to the equations of slightly compressible fluid dynamics to obtain a generalized form of the acoustics equations that describe the first-order correction to incompressible flow. The special case of a barotropic fluid was analyzed previously by Klainerman and Majda.