Stability of viscous scalar shock fronts in several dimensions

Author:
Jonathan Goodman

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

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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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DOI:
https://doi.org/10.1090/S0002-9947-1989-0978372-9

Article copyright:
© Copyright 1989
American Mathematical Society