On the structure of solutions of a class of hyperbolic systems with several spatial variables in the far field


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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.

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A. Nesterov

Moscow City Pedagogical University

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Email: andrenesterov@yandex.ru
俄罗斯联邦, Vtoroy Sel’skokhozyaistvennyi proezd 4, Moscow, 129226

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