An Oleinik inequality for a class of heterogeneous balance laws

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Abstract

Although an Oleinik inequality is not expected for general heterogeneous scalar balance laws, there is a favorable case, when the source term g(x) is smooth and nondecreasing. In this setting, we are able to obtain an Oleinik-type inequality and, consequently, a smoothing effect.

Keywords

balance laws / entropy solution / strictly convex flux / Oleinik inequality / wave interaction / generalized Riemann problem / regularizing effect

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