  The present paper is concerned with the Cauchy-Dirichlet problem for
fractional (and non-fractional) nonlinear diffusion equations posed in bounded
domains. Main results consist of well-posedness in an energy class with no sign
restriction and convergence of such (possibly sign-changing) energy solutions
to asymptotic profiles after a proper rescaling. They will be proved in a
variational scheme only, without any use of semigroup theories nor classical
quasilinear parabolic theories. Proofs are self-contained and performed in a
totally unified fashion for both fractional and non-fractional cases as well as
for both porous medium and fast diffusion cases.
