On the stability functional for conservation laws. (English) Zbl 1157.35423
Summary: This note is devoted to the explicit construction of a functional defined on all pairs of \(\mathbf L^{\mathbf 1}\) functions with small total variation, which is equivalent to the \(\mathbf L^{\mathbf 1}\) distance and non-increasing along the trajectories of a given system of conservation laws. Two different constructions are provided, yielding an extension of the original stability functional of Bressan, Liu and Yang [A. Bressan, T.-P. Liu and T. Yang, Arch. Ration. Mech. Anal. 149, No. 1, 1–22 (1999; Zbl 0938.35093)].
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
explicit constructionCitations:
Zbl 0938.35093References:
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