2 problems

Further-inequality conjecture. Some further $\Lambda$-convex inequality should be added to $U$ so as to reduce it appropriately and exclude the case

Let $\bar{\mathbf U}_{ij}^{n+1}$ be the updated cell-average state, and let $\bar{\mathbf U}_{i,j}^n$, $\bar{\mathbf U}_{i\pm1,j}^n$, and $\bar{\mathbf U}_{i,j\pm1}^n$ denote the c…