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.
|Original language||English (US)|
|Number of pages||13|
|Journal||Transactions of the American Mathematical Society|
|State||Published - Feb 1989|
ASJC Scopus subject areas
- Applied Mathematics