Global algebras of nonlinear generalized functions with applications in general relativity

We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of generalized functions and tensor fields. We furthermore provide a survey on possible applications in general relativity in light of the limitations of distribution theory

Almost periodic evolution systems with impulse action at state-dependent moments

We study the existence of almost periodic solutions for semi-linear abstract parabolic evolution equations with impulse action at state-dependent moments. In particular, we present conditions excluding the beating phenomenon in these systems. The main result is illustrated with an example of impulsive diffusive logistic equation.Comment: 16 pages, minor changes from the previous versio