CLASSIFICATION OF NONNEGATIVE TRAVELING WAVE SOLUTIONS FOR THE 1D DEGENERATE PARABOLIC EQUATIONS

Traveling wave solutions for the one-dimensional degenerate parabolic equations are considered. The purpose of this paper is to classify the nonnegative traveling wave solutions including sense of weak solutions of these equations and to present their existence, information about their shape and asymptotic behavior. These are studied by applying the framework that combines Poincare compactification and classical dynamical systems theory. We also aim to use these results to generalize the results of our previous studies. The key to this is the introduction of a transformation, which overcomes the generalization difficulties faced by these studies.