The error in spatial truncation for systems of parabolic conservation laws

Kuo, Hung Ju

doi:10.1090/S0002-9947-1989-0978364-X

The error in spatial truncation for systems of parabolic conservation laws
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Trans. Amer. Math. Soc. 311 (1989), 433-465 Request permission

Abstract:

In this paper we investigate the behavior of the solution of \[ \begin {array}{*{20}{c}} {{u_t} = D{u_{xx}} - f{{(u)}_x},} \\ {u(0,x) = {u_0}(x) \in {L^\infty },\qquad u(t, \pm L) = {u^ \pm },} \\ \end {array} \] where $t \geqslant 0$ and $x \in [ - L,L]$. Solutions of this equation are considered to be approximations to the solutions of the corresponding parabolic conservation laws. We obtain decay results on the norms of the difference between the solution for $L$ infinite and the solution when $L$ is finite.

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Spatial truncation and finite difference schemes for systems of parabolic conservation laws

Linear and quasi-linear equations of parabolic type

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