Construction of unbounded entropy solution of Cauchy problem with a countable number of shock waves (Q1584127)
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scientific article; zbMATH DE number 1524034
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Construction of unbounded entropy solution of Cauchy problem with a countable number of shock waves |
scientific article; zbMATH DE number 1524034 |
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Construction of unbounded entropy solution of Cauchy problem with a countable number of shock waves (English)
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31 October 2000
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The author proposes a method of constructing the generalized entropy solution to the Cauchy problem for the equation \[ u_t+u^2u_x = uu_t+(f(u))_x = 0,\quad t>0,\quad x\in \mathbb{R}, \] where \( f(u)=u^3/3\), with linear initial data. For example, \( u\big|_{t=0} = u_0(x)\equiv x/2.\) The solution has a countable number of strong discontinuity lines (shock waves).
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countable number of strong discontinuity lines
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