Article
MSC:
35L60,
47J25,
65J15,
65N12 | MR 2025295 | Zbl 1099.65049 | DOI: 10.1023/B:APOM.0000024483.00505.79
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Summary:
Weak solutions of given problems are sometimes not necessarily unique. Relevant solutions are then picked out of the set of weak solutions by so-called entropy conditions. Connections between the original and the numerical entropy condition were often discussed in the particular case of scalar conservation laws, and also a general theory was presented in the literature for general scalar problems. The entropy conditions were realized by certain inequalities not generalizable to systems of equations in a trivial way. It is a concern of this article to extend the theory in such a way that inequalities can be replaced by general relations, and this not only in an abstract way but also realized by examples.
References:
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