The Error in Spatial Truncation for Systems of Parabolic Conservation Laws

In this paper we investigate the behavior of the solution of \begin{equation*} \begin{split} u_t = Du_{xx} - f(u)_x, \\ u(0, x) = u_0(x) \in L^\infty, & u(t, \pm L) = u^\pm, \end{split} \end{equation*} where $t \geq 0$ and $x \in \lbrack -L, L \rbrack$. Solutions of this equation are considered...

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