Asymptotic behavior for the viscous Burgers equation with a stationary source (Q2832703)
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scientific article; zbMATH DE number 6652574
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic behavior for the viscous Burgers equation with a stationary source |
scientific article; zbMATH DE number 6652574 |
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Asymptotic behavior for the viscous Burgers equation with a stationary source (English)
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14 November 2016
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initial-value problem
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nonlinear convection
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Véron measure
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gas dynamics
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The paper addresses solutions of the Burgers equation with a stationary driving term \(f(x)\) which is localized on a compact support: NEWLINE\[NEWLINE u_t + (u^2)_x - u_{xx} = f(x), NEWLINE\]NEWLINE with an initial condition at \(t=0\). The paper produces a rigorous proof of the statement that the evolving solution locally converges to a stationary positive bounded steady state. Because the presence of the stationary source does not make it possible to use the boundedness of the solutions' norm in time, a measure of the Véron type is used.
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