SOLUTIONS CONTAINING A LARGE PARAMETER OF A QUASI-LINEAR HYPERBOLIC SYSTEM OF EQUATIONS AND THEIR NONLINEAR GEOMETRIC OPTICS APPROXIMATION

It is well known that a quasi-linear first order strictly hyperbolic s ystem of partial differential equations admits a formal approximate so lution with the initial data lambda-1 a0(lambdax . eta, x)r1(eta), lam bda > 0, x, eta is-an-element-of R(n), eta not-equal 0. Here r1(eta) i s a characteristic vector, and a0(sigma, x) is a smooth scalar functio n of compact support. Under the additional requirements that n = 2 or 3 and that a0(simga, x) have the vanishing mean with respect to simga, it is shown that a genuine solution exists in a time interval indepen dent of lambda, and that the formal solution is asymptotic to the genu ine solution as lambda --> infinity.