Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case
We consider a scalar hyperbolic conservation law with a nonlinear source term and viscosity $varepsilon$. For $varepsilon=0$, there exist in general different types of heteroclinic entropy traveling waves. It is shown that for $varepsilon>0$ sufficiently small the viscous equation possesses simil...
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| Format: | Article |
| Language: | English |
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Texas State University
2000-04-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2000/30/abstr.html |
| Summary: | We consider a scalar hyperbolic conservation law with a nonlinear source term and viscosity $varepsilon$. For $varepsilon=0$, there exist in general different types of heteroclinic entropy traveling waves. It is shown that for $varepsilon>0$ sufficiently small the viscous equation possesses similar traveling wave solutions and that the profiles converge in exponentially weighted $L^1$-norms as $varepsilon$ decreases to zero. The proof is based on a careful study of the singularly perturbed second-order equation that arises from the traveling wave ansatz. |
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| ISSN: | 1072-6691 |