Dr. Vita Leonessa “On the approximation of solutions of evolution problems by means of positive linear operators”

Given a class of degenerate second-order elliptic differential operators,
by using some techniques arising from approximation theory it is
possible to show that they generate strongly continuous semigroups
which can be approximated by means of suitable positive linear
operators. The resulting approximation formula can be used in the study
of preservation properties and the asymptotic behaviour of the
semigroup and, as a consequence, of spatial regularity properties and
asymptotic behaviour of the solution of the differential problem.

During the talk we shall present some results obtained in collaboration with F. Altomare (Univ. of Bari), M. Cappelletti Montano (Univ. of Bari), and I. Raşa (Tech. Univ. of Cluj-Napoca).