The goal of this paper is to construct explicitly the global attractors of quasilinear parabolic
equations, as it was done for the semilinear case by Brunovský and Fiedler (1986)[8], and
generalized by Fiedler and Rocha (1996)[13]. In particular, we construct heteroclinic
connections between hyperbolic equilibria, stating necessary and sufficient conditions for
heteroclinics to occur. Such conditions can be computed through a permutation of the
equilibria. Lastly, an example is computed yielding the well known Chafee-Infante attractor.

The goal of this paper is to construct explicitly the global attractors of parabolic equations
with singular diffusion coefficients on the boundary, as it was done without the singular term
for the semilinear case by Brunovský and Fiedler (1986), generalized by Fiedler and Rocha
(1996) and later for quasilinear equations by Lappicy (2017). In particular, we construct
heteroclinic connections between hyperbolic equilibria, stating necessary and sufficient
conditions for heteroclinics to occur. Such conditions can be computed through a …