Abstract

3) Michael Röckner (Bielefeld University and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing) Joint work with Wei Liu (Jiangsu Normal University, Xuzhou) and Jos\’e Lu\’is da Silva (University of Madeira, Funchal) Title: Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations Abstract: In this talk we shall identify generalized time-fractional derivatives as generators of $C_0$-operator semigroups and prove their strong dissipativity on Gelfand triples of properly in time weighted $L^2$-path spaces. In particular, the classical Caputo derivative is included as a special case. As a consequence, one obtains the existence and uniqueness of solutions to evolution equations on Gelfand triples with generalized time-fractional derivatives. These equations are of type \begin{equation} \frac{d}{dt} (k u)(t) + A(t, u(t)) = f(t), \quad 0