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Modeling the influence of small-scale dispersion processes in a continuum on the formation of large-scale phenomena. (Russian, English) Zbl 1136.35421
Zh. Vychisl. Mat. Mat. Fiz. 44, No. 6, 1119-1126 (2004); translation in Comput. Math. Math. Phys. 44, No. 6, 1062-1068 (2004).
Solutions and their long-time asymptotics are found numerically in the Cauchy problem for a model equation taking into account nonlinearity, dispersion, and dissipation, with the initial data specified in the form of a smoothed step.

35L60 First-order nonlinear hyperbolic equations
35B20 Perturbations in context of PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
35L67 Shocks and singularities for hyperbolic equations
76R99 Diffusion and convection
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