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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The error in spatial truncation for systems of parabolic conservation laws
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by Hung Ju Kuo PDF
Trans. Amer. Math. Soc. 311 (1989), 433-465 Request permission

Abstract:

In this paper we investigate the behavior of the solution of \[ \begin {array}{*{20}{c}} {{u_t} = D{u_{xx}} - f{{(u)}_x},} \\ {u(0,x) = {u_0}(x) \in {L^\infty },\qquad u(t, \pm L) = {u^ \pm },} \\ \end {array} \] 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
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 433-465
  • MSC: Primary 65M15; Secondary 35K55, 35L65, 65N15
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0978364-X
  • MathSciNet review: 978364