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Weighted-\(L^ 2\) stability of traveling waves in a porous medium. (English) Zbl 0870.35083

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)

MSC:

35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
35B35 Stability in context of PDEs
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