We consider a system of nonlinear diffusion equations modelling (isothermal) phase segregation of an ideal mixture of
N
≥
2
components occupying a bounded region
Ω
⊂
R
d
,
d
≤
3
. Our system is ...subject to a constant mobility matrix of coefficients, a free energy functional given in terms of
singular entropy
generated potentials and
localized
capillarity effects. We prove well-posedness and regularity results which generalize the ones obtained by Elliott and Luckhaus (IMA Preprint Ser 887, 1991). In particular, if
d
≤
2
, we derive the uniform strict separation of solutions from the singular points of the (entropy) nonlinearity. Then, even if
d
=
3
, we prove the existence of a global (regular) attractor as well as we establish the convergence of solutions to single equilibria. If
d
=
3
, this convergence requires the validity of the asymptotic strict separation property. This work constitutes the first part of an extended three-part study involving the phase behavior of multi-component systems, with a second part addressing the presence of nonlocal capillarity effects, and a final part concerning the numerical study of such systems along with some relevant application.
