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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.
Received: 23.03.2001
Citation:
V. S. Alekseev, “Hyperbolic Regularization of the Sobolev System”, Mat. Tr., 5:1 (2002), 3–17; Siberian Adv. Math., 12:3 (2003), 1–15
Linking options:
https://www.mathnet.ru/eng/mt96 https://www.mathnet.ru/eng/mt/v5/i1/p3
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Abstract page: | 269 | Full-text PDF : | 115 | References: | 44 | First page: | 1 |
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