Stability of traveling waves of a solute transport equation
The author proves the large time asymptotic stability of traveling wave solutions to the scalar solute transport equation (containment transport equation) with spatially periodic diffusion-adsorption coefficients in one space dimension. The time dependent solutions converge in proper norms to a translate of traveling wave solutions as time approaches infinity. In case of classical traveling waves, the convergence rate is exponential in time for a class of small initial perturbations, and for general order one perturbations, the convergence holds in supremum norm. In case of degenerate Hölder continuous traveling waves, the convergence holds in \(L^1\) norm. As a byproduct, uniqueness up to translation of degenerate traveling waves follows. Maximum principle, \(L^1\) contraction spectral theory, and a space-time invariance property of solutions are used in this article.
spatially periodic diffusion-adsorption coefficients
scientific article; zbMATH DE number 1014439
scientific article