Shock waves for the hyperbolic balance laws with discontinuous sources (Q2922238)
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scientific article; zbMATH DE number 6353364
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Shock waves for the hyperbolic balance laws with discontinuous sources |
scientific article; zbMATH DE number 6353364 |
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Shock waves for the hyperbolic balance laws with discontinuous sources (English)
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9 October 2014
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weak discontinuities
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local existence
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The authors study shock wave solutions to the Cauchy problem for the \(2\times 2\) hyperbolic system of balance laws \(\partial_t U+\partial_x f(U)=g(t,x)\), with both the initial function \(U_0(x)\) and the source function \(g(t,x)\) being discontinuous only at \(x=0\). Under some structural assumptions they prove the existence of a local weak solution containing a shock wave, which follows a weak (contact) discontinuity \(x=0\) created under the influence of the discontinuous source term.
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