Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media
We prove the existence of multidimensional traveling-wave solutions to the scalar equation for the transport of solutes (contaminants) with nonlinear adsorption and spatially periodic convection-diffusion- adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the Lax and Oleinik entropy conditions. In the nondegenerate case, we also prove the uniqueness of the traveling waves. We use the sliding domain method, the continuation method, spectral theory, maximum principles, and a priori estimates. In the degenerate case, the traveling waves are weak solutions of a degenerate parabolic equation and are only Hölder continuous. We obtain them by taking suitable limits on the nondegenerate traveling waves.
periodic convection-diffusion-adsorption coefficients
scientific article; zbMATH DE number 754024
scientific article