On the asymptotics of the solution to a singularly perturbed system of first-order partial differential equations with small nonlinearity in the critical case
Abstract:
A complete asymptotic expansion of the solution to an initial value problem for a singularly perturbed system of hyperbolic equations is constructed and justified. A specific feature of the problem is that its solution has a wavelet zone in a neighborhood of which the asymptotics is described by a parabolic equation.
Key words:initial value problems, singular perturbations, Cauchy problem, hyperbolic systems of equations, asymptotic representation of solutions, parabolic layer.
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