Well-posedness for a class of \(2\times 2\) conservation laws with \(\mathbb{L}^\infty\) data (Q1370991)
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scientific article; zbMATH DE number 1080202
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Well-posedness for a class of \(2\times 2\) conservation laws with \(\mathbb{L}^\infty\) data |
scientific article; zbMATH DE number 1080202 |
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Well-posedness for a class of \(2\times 2\) conservation laws with \(\mathbb{L}^\infty\) data (English)
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3 August 1998
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The following special class od \(2\times 2\) systems of conservation laws is considered: \(u_t+f(u,v)_x=0\), \(v_t=0\). The initial data for these systems are supposed to be in \(L^1\cap L^\infty\). The existence of a weak solution to such a Cauchy problem is proved in the strictly hyperbolic case. This solution depends continuously in \(L^1\)-norm on initial data and can be characterized in terms of a Kružkov-type entropy condition.
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Kružkov-type entropy condition
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