Geodesic
Hyperbolic Regularization of the~Sobolev System
Matematičeskie trudy, Tome 5 (2002) no. 1, pp. 3-17.

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The article deals with a hyperbolic system with small parameter which turns into a Sobolev system as the parameter vanishes. It is proven that some components of a solution to the Cauchy problem for this hyperbolic system tend to the corresponding components of a solution to the Cauchy problem for the Sobolev system uniformly on the set $[0,T]\times\mathbb R_3$. The derivatives with respect to the space variables of the remaining component converge uniformly on every set $[t_0,T]\times K$, where $0$ and $K$ is a compact set. 
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V. S. Alekseev. Hyperbolic Regularization of the~Sobolev System. Matematičeskie trudy, Tome 5 (2002) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/MT_2002_5_1_a0/

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