The aim of these notes is to include in a uniform presentation style several topics related to
the theory of degenerate nonlinear diffusion equations treated in the mathematical framework
of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems
concern nonlinear parabolic equations involving two cases of degeneracy. More precisely one
case is due to the vanishing of the time derivative coefficient and the other is provided by
the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From
the mathematical point of view the results presented in these notes can be considered as
general results in the theory of degenerate nonlinear diffusion equations. However this work
does not seek to present an exhaustive study of degenerate diffusion equations but rather to
emphasize some rigorous and efficient techniques for approaching various problems involving
degenerate nonlinear diffusion equations such as well-posedness periodic solutions
asymptotic behaviour discretization schemes coefficient identification and to introduce
relevant solving methods for each of them.
