Viscous Profiles for Traveling Waves of Scalar Balance Laws: The Uniformly Hyperbolic Case
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We consider a scalar hyperbolic conservation law with a nonlinear source term and viscosity ɛ. For ɛ = 0, there exist in general different types of heteroclinic entropy traveling waves. It is shown that for ɛ positive and sufficiently small the viscous equation possesses similar traveling wave solutions and that the profiles converge in exponentially weighted L1-norms as ɛ ↘ zero. The proof is based on a careful study of the singularly perturbed second-order equation that arises from the traveling wave ansatz.
CitationHaerterich, J. (2000). Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case. Electronic Journal of Differential Equations, 2000(30), pp. 1-22.
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