Logan, J. David Weighted-\(L^ 2\) stability of traveling waves in a porous medium. (English) Zbl 0870.35083 Commun. Appl. Nonlinear Anal. 4, No. 1, 55-62 (1997). The author gives an analytic proof of the stability of a travelling wave profile for a nonlinear equation that models the convection and diffusion of a chemical solution in a porous medium. The method is based on geometric methods and an energy argument. In addition to the energy argument a proof based on a maximum principle is presented. To obtain the stability result one restricts the perturbations to a weighted \(L^2\)-space. Reviewer: V.A.Sava (Iaşi) Cited in 1 Document MSC: 35Q35 PDEs in connection with fluid mechanics 76S05 Flows in porous media; filtration; seepage 35B35 Stability in context of PDEs Keywords:stability of a travelling wave profile; convection and diffusion of a chemical solute in a porous medium PDFBibTeX XMLCite \textit{J. D. Logan}, Commun. Appl. Nonlinear Anal. 4, No. 1, 55--62 (1997; Zbl 0870.35083)