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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Stability of viscous scalar shock fronts in several dimensions
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by Jonathan Goodman
Trans. Amer. Math. Soc. 311 (1989), 683-695
DOI: https://doi.org/10.1090/S0002-9947-1989-0978372-9
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Abstract:

We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.
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Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 683-695
  • MSC: Primary 35K30; Secondary 35B35, 35L67
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0978372-9
  • MathSciNet review: 978372