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Relative entropy method applied to the stability of shocks for systems of conservation laws

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Partial Differential Equations in Kinetic Theories

We develop a theory based on relative entropy to show stability and uniqueness of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of big amplitude), among bounded entropic weak solutions having an additional strong trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, the strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.

This talk is part of the Isaac Newton Institute Seminar Series series.

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