Stability of viscous scalar shock fronts in several dimensions
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 Trans. Amer. Math. Soc. 311 (1989), 683695 Request permission
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.References

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Additional Information
 © Copyright 1989 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 311 (1989), 683695
 MSC: Primary 35K30; Secondary 35B35, 35L67
 DOI: https://doi.org/10.1090/S00029947198909783729
 MathSciNet review: 978372