Computing Qualitatively Correct Approximations of Balance Laws by Laurent Gosse

Author:Laurent Gosse
Language: eng
Format: epub
Publisher: Springer Milan, Milano

And this is enough to conclude since BV(ℝ) ⊂ L∞(ℝ).□

By standard arguments, we can establish strong L loc 1 compactness for f Δx ± as Δx → 0 relying on the bound stated in Lemma 8.5.

Remark 8.3.

The bounds derived in Lemma 8.5 are not very good since they contain exponential terms which result from the use of the classical Gronwall Lemma. This is a consequence of the lack of Temple-type structure, meaning in particular that the total variation of Riemann invariants for (8.12) doesn’t decay with time.

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