Abstract
The equations of isothermal gas dynamics are expressed as a 2×2-system of genuinely nonlinear hyperbolic conservation laws which possesses a convex entropy. Existence of weak global solutions is known for even large initial data via Glimm’s difference scheme. We show that the total variation of such (large) solutions decays strongly to zero. The proof consists in showing that the total amount of wave interaction in the Glimm approximations is uniformly bounded.
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Asakura, F. Decay of solutions for the equations of isothermal gas dynamics. Japan J. Indust. Appl. Math. 10, 133–164 (1993). https://doi.org/10.1007/BF03167207
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DOI: https://doi.org/10.1007/BF03167207