Asymptotics for symmetric hyperbolic systems with a large parameter (Q1826023)

From author's abstract: The asymptotic behavior as \(\lambda\) \(\to \infty\) is analysed for solutions u(\(\lambda)\) of quasilinear symmetric hyperbolic systems of the form \[ A^ 0u_ t+A^ ju_{x_ j}+\lambda C^ ju_{x_ j}=F;\quad u(0,x,\lambda)=u_ 0(x,\lambda), \] where the \(A^ k\) and F depend on t,x,u, and u/\(\lambda\), but the \(C^ j\) 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 in incompressible flow. The special case of a barotropic fluid was analyzed previously by Klainerman and Majda.