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Yingjie Wang
2026-04-10 01:56:05 -04:00
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@@ -823,8 +823,9 @@ $}
\] \]
where $c_1$, $c_2$, $c_3$ and $c_4$ are positive constants that large enough (the lower bound can be calculated). Thus we have constraint damping. where $c_1$, $c_2$, $c_3$ and $c_4$ are positive constants that large enough (the lower bound can be calculated). Thus we have constraint damping.
\vspace{0.5cm} \vspace{0.2cm}
{\color{red} \textbf{Unfortunately, this naive system is not even weakly hyperbolic!}} {\color{red} \textbf{Unfortunately, this naive system is not even weakly hyperbolic!}}
\vspace{0.2cm}
We have to add some constraint terms that equals to zero, while contributes to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues. This is the most tricky part, and we have to do it by hand, which is very time consuming and error prone. We have to add some constraint terms that equals to zero, while contributes to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues. This is the most tricky part, and we have to do it by hand, which is very time consuming and error prone.
\end{frame} \end{frame}