Hyperbolic Regularization of the Sobolev System

V. S. Alekseev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: 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 $0<t_0<T$ and $K$ is a compact set.

Key words: Cauchy problem, Sobolev system, hyperbolic system with small parameter.

UDC: 517.955

Received: 23.03.2001

 English version: Siberian Advances in Mathematics, 2003, 12:3, 1–15

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