Viscous Profiles for Traveling Waves of Scalar Balance Laws: The Uniformly Hyperbolic Case
Southwest Texas State University, Department of Mathematics
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.
Hyperbolic conservation laws, Source terms, Traveling waves, Viscous profiles, Singular perturbations
Haerterich, 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.