The promising increase of Electric Vehicles (EVs) in our society poses a challenging problem on the impact assessment their charging/discharging to power distribution grids. This paper addresses framework nonlinear differential equations. Specifically, we address ODE (Ordinary Differential Equation) model for representing spatial profile voltage phasor along feeder, which has been recently intr...

We study the Schrödinger–Poisson–Slater equation ? ? u + ? ( I 2 ? | ) = p in R 3 , where ? 6 and > 0 . By using direct variational analysis based on comparison of ground state energy levels, we obtain a characterization limit profile positive states for ? ?

We study atomic chains with nonlinear nearest neighbour interactions and prove the existence of fronts (heteroclinic travelling waves with constant asymptotic states). Generalizing recent results of Herrmann and Rademacher we allow for non-convex interaction potentials and find fronts with non-monotone profile. These fronts minimize an action integral and can only exists if the asymptotic state...

We investigate the long-time behavior of a wave packet initially localized at a single site n₀ in translationally invariant harmonic and anharmonic chains with random interactions. In the harmonic case, the energy profile averaged on time and disorder decays for large |n-n₀| as a power law ≈ C|n-n₀|(⁻η), where η=⁵/₂ and ³/₂ for initial displacement and momentum excitations, ...

In this paper, we study the asymptotic (large time) behavior of a selection-mutation-competition model for a population structured with respect to a phenotypic trait, when the rate of mutation is very small. We assume that the reproduction is asexual, and that the mutations can be described by a linear integral operator. We are interested in the interplay between the time variable t and the rat...

This paper considers discrete and differential nonlinear repetitive processes using the state-space model setting. These processes are a particular class of 2D systems that have their origins in the modeling of physical processes. Their distinguishing characteristic is that one of the two independent variables needed to describe the dynamics evolves over a finite interval and therefore they are...

In this paper, we study the asymptotic (large time) behavior of a selection-mutation-competition model for a population structured with respect to a phenotypic trait when the rate of mutation is very small. We assume that the reproduction is asexual, and that the mutations can be described by a linear integral operator. We are interested in the interplay between the time variable t and the rate...

Numerous numerical studies indicate that dark matter halos show an almost universal radial density profile. The origin of the profile is still under debate. We investigate this topic and pay particular attention to the velocity dispersion profile. To this end we have performed high-resolution simulations with two independent codes, ART and Gadget. The radial velocity dispersion can be approxima...

Osaki and Yagi (2001) give a proof of global existence for the classical chemotaxis model in one space dimension with use of energy estimates. Here we present an alternative proof which uses the regularity properties of the heat-equation semigroup. With this method we can identify a large selection of admissible spaces, such that the chemotaxis model de nes a global semigroup on these spaces. W...