Geodesic
𝐿₁ stability for 2×2 systems of hyperbolic conservation laws
Liu, Tai-Ping1 ; Yang, Tong2
1 Department of Mathematics, Stanford University, Stanford, California 94305-2060
2 Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Journal of the American Mathematical Society, Tome 12 (1999) no. 3, pp. 729-774

Voir la notice de l'article provenant de la source American Mathematical Society

In this paper, we study the evolution of the $L_1$ distance of solutions for systems of $2\times 2$ hyperbolic conservation laws. For the approximate solutions constructed by Glimm’s scheme with the aid of the wave tracing method, we introduce a nonlinear functional which is equivalent to the $L_1$ distance between solutions, nonincreasing in time, and expressed explicitly in terms of the wave patterns of the solutions. This functional reveals the nonlinear mechanism of wave interactions and coupling which affect the $L_1$ topology.
DOI : 10.1090/S0894-0347-99-00292-1

Liu, Tai-Ping 1 ; Yang, Tong 2

1 Department of Mathematics, Stanford University, Stanford, California 94305-2060
2 Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong 
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Liu, Tai-Ping; Yang, Tong. 𝐿₁ stability for 2×2 systems of hyperbolic conservation laws. Journal of the American Mathematical Society, Tome 12 (1999) no. 3, pp. 729-774. doi: 10.1090/S0894-0347-99-00292-1

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