Abstract
We prove nonlinear stability in L1 of planar shock front solutions to a viscous conservation law in two spatial dimensions and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an effective diffusion coefficient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the linearized problem.
Original language | English (US) |
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Pages (from-to) | 255-277 |
Number of pages | 23 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - 1999 |
Keywords
- Long-time behavior
- Shock fronts
- Viscous conservation law
ASJC Scopus subject areas
- Analysis