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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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Stability of viscous scalar shock fronts in several dimensions
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by Jonathan Goodman PDF
Trans. Amer. Math. Soc. 311 (1989), 683-695 Request permission


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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 683-695
  • MSC: Primary 35K30; Secondary 35B35, 35L67
  • DOI:
  • MathSciNet review: 978372