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KIAM Preprint № 90, Moscow, 2016
Authors: Ilyin A. A., Rykov Y. G.
On the closeness of trajectories for model quasi-gasdynamic equations. Linear case
Abstract:
On a model example of a linear hyperbolic equation with small parameter multiplying the highest time derivative it is shown that the closeness of individual trajectories to the dynamics of the limiting parabolic equation essentially depends on the Fourier spectra of the initial data. We prove explicit estimates for the closeness of the solutions in the uniform norms and in the norms of the Sobolev spaces of arbitrary smoothness. We consider both the mutidimensional space-periodic case and the case of a bounded domain.
Keywords:
quasi-gasdynamic equations, hyperbolization, Fourier spectrum, closeness of trajectories
Publication language: russian,  pages: 14
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Ilyin Alexei Andreevich,  KIAM RAS
  • Rykov Yuri Germanovich,  orcid.org/0000-0003-1695-6202KIAM RAS