Weak stability in the global $L^ 1$-norm for systems of hyperbolic conservation laws

Author:
Blake Temple

Journal:
Trans. Amer. Math. Soc. **317** (1990), 673-685

MSC:
Primary 35L65; Secondary 35B35

DOI:
https://doi.org/10.1090/S0002-9947-1990-0948199-0

MathSciNet review:
948199

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Abstract: We prove that solutions for systems of two conservation laws which are generated by Glimm’s method are weakly stable in the global ${L^1}$-norm. The method relies on a previous decay result of the author, together with a new estimate for the ${L^1}$ Lipschitz constant that relates solutions at different times. The estimate shows that this constant can be bounded by the supnorm of the solution, and is proved for any number of equations. The techniques do not rely on the existence of a family of entropies, and moreover the results would generalize immediately to more than two equations if one were to establish the stability of solutions in the supnorm for more than two equations.

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© Copyright 1990
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