| Abstract: |
| We study a generalized conservative Burgers equation on a $n$-dimensional torus. We first consider the associated linear system. By exploiting the Harnack inequality and the $L^1$ contraction property, we establish exponential stability in the $L^1$ norm. For the nonlinear problem, we derive a uniform-in-time estimate of the solution using the De Giorgi-Nash-Moser iteration method. Moreover, we show that the H\older norm of the solution remains uniformly bounded and decays exponentially. |
|