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This paper reports results on the classification of traveling wave solutions,including nonnegative weak sense, in the spatial 1D degenerate parabolicequation. These are obtained through dynamical systems theory and geometricapproaches (in particular, Poincar\'e compactification). Classification oftraveling wave solutions means enumerating those that exist and presentingproperties of each solution, such as its profile and asymptotic behavior. Theresults examine a different range of parameters included in the equation, usingthe same techniques as discussed in the earlier work [Y. Ichida, DiscreteContin. Dyn. Syst., Ser. B, {\bf{28}} (2023), no. 2, 1116--1132]. In a cleardeparture from this previous work, the classification results obtained in thispaper and the successful application of known transformation also yield resultsfor the classification of (weak) nonnegative traveling wave solutions forspatial 1D porous medium equations with special nonlinear terms and thesimplest porous medium equation. Finally, the bifurcations at infinity occur inthe two-dimensional ordinary differential equations that characterize thesetraveling wave solutions are shown.

Classification of nonnegative traveling wave solutions for certain 1D degenerate parabolic equation and porous medium equation