Related papers: Asymptotic behaviors for the compressible Euler sy…

This paper revisits the previously proposed linear asymptotic observer of the motion state variables with nonlinear friction and provides a robust design suitable for both, transient presliding and steady-state sliding phases of the…

We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The…

We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditions for asymptotic flocking of the solutions. These…

We consider the (barotropic) Euler system describing the motion of a compressible inviscid fluid driven by a stochastic forcing. Adapting the method of convex integration we show that the initial value problem is ill-posed in the class of…

We extend the analysis developed in [33] in order to prove convergence to consensus results for a Cucker-Smale type model with hierarchical leadership and distributed delay. Flocking estimates are obtained for a general interaction…

We present an analytical and numerical study of the coherent exciton polarization including exciton-exciton correlation. The time evolution after excitation with ultrashort optical pulses can be divided into a slowly varying polarization…

We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensionnal model of active particles. We…

As a Newtonian cosmological model the Vlasov-Poisson-Boltzmann system is considered, and a slightly modified Boltzmann equation, which describes the stability of an expanding universe, is derived. Asymptotic behaviour of solutions turns out…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and…

We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…

With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…

The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…

For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…

We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…

Emergent phenomena are ubiquitous in nature and refer to spatial, temporal, or spatiotemporal pattern formation in complex nonlinear systems driven out of equilibrium that is not contained in the microscopic descriptions at the…

A class of parabolic-parabolic Keller-Segel systems with degenerate diffusion and volume filling is studied in a bounded domain subject to no-flux boundary conditions. The equations are derived from a multiphase fluid model. The interplay…

We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…

This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible…

We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a non-perturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the…