Stability for weighted composition $C_0$-semigroups on Lebesgue and   Sobolev spaces
  Stability of weighted composition strongly continuous semigroups acting on Lebesgue and Sobolev spaces is studied, without the use of spectral conditions on the generator of the semigroup. Applications to the generalized von Foerster - Lasota semigroup and a comparison with hypercylicity conditions are presented.\ 
Javier Aroza, Elisabetta Mangino
math.FA