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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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Weak stability in the global $L^ 1$-norm for systems of hyperbolic conservation laws
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by Blake Temple PDF
Trans. Amer. Math. Soc. 317 (1990), 673-685 Request permission

Abstract:

We prove that solutions for systems of two conservation laws which are generated by Glimm’s method are weakly stable in the global ${L^1}$-norm. The method relies on a previous decay result of the author, together with a new estimate for the ${L^1}$ Lipschitz constant that relates solutions at different times. The estimate shows that this constant can be bounded by the supnorm of the solution, and is proved for any number of equations. The techniques do not rely on the existence of a family of entropies, and moreover the results would generalize immediately to more than two equations if one were to establish the stability of solutions in the supnorm for more than two equations.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 317 (1990), 673-685
  • MSC: Primary 35L65; Secondary 35B35
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0948199-0
  • MathSciNet review: 948199