Harterich, Jorg2019-12-182019-12-182000-04-25Haerterich, J. (2000). Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case. <i>Electronic Journal of Differential Equations, 2000</i>(30), pp. 1-22.1072-6691https://hdl.handle.net/10877/9106We 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.Text22 pages1 file (.pdf)enAttribution 4.0 InternationalHyperbolic conservation lawsSource termsTraveling wavesViscous profilesSingular perturbationsArticle