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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The error in spatial truncation for systems of parabolic conservation laws


Author: Hung Ju Kuo
Journal: Trans. Amer. Math. Soc. 311 (1989), 433-465
MSC: Primary 65M15; Secondary 35K55, 35L65, 65N15
MathSciNet review: 978364
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Abstract: In this paper we investigate the behavior of the solution of

\begin{displaymath}\begin{array}{*{20}{c}} {{u_t} = D{u_{xx}} - f{{(u)}_x},} \\ ... ...in {L^\infty },\qquad u(t, \pm L) = {u^ \pm },} \\ \end{array} \end{displaymath}

where $ t \geqslant 0$ and $ x \in [ - L,L]$. Solutions of this equation are considered to be approximations to the solutions of the corresponding parabolic conservation laws. We obtain decay results on the norms of the difference between the solution for $ L$ infinite and the solution when $ L$ is finite.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0978364-X
PII: S 0002-9947(1989)0978364-X
Article copyright: © Copyright 1989 American Mathematical Society