On the asymptotics of the solution to a singularly perturbed hyperbolic system of equations with several spatial variables in the critical case

A complete asymptotic expansion of the solution to an initial value problem for a singularly perturbed hyperbolic system of equations in several spatial variables is constructed and justified. A specific feature of the problem is that its solution has a spike zone in a neighborhood of which the asymptotics is described by a parabolic equation.