Abstract:
An asymptotic expansion of the solution to the Cauchy problem for a class of hyperbolic weakly nonlinear systems with many spatial variables is constructed. A parabolic quasilinear equation describing the behavior of the solution at asymptotically large values of the independent variables is obtained. The pseudo-diffusion processes that depend on the relationship between the number of equations and the number of spatial variables are analyzed. The structure of the subspace in which there are pseudo-diffusion evolution processes of the solution in the far field is described.
Key words:hyperbolic systems, Cauchy problem, small nonlinearity, asymptotics in the far field, parabolic equations, critical case.
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