Nonlinear Stability of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Dimensions One and Two
Nonlinear Stability of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Dimensions One and Two
Extending results of Oh and Zumbrun in dimensions $d\geq3$, we establish nonlinear stability and asymptotic behavior of spatially periodic traveling-wave solutions of viscous systems of conservation laws in critical dimensions $d=1,2$, under a natural set of spectral stability assumptions introduced by Schneider in the setting of reaction diffusion equations. The …