Related papers: Equilibria of biological aggregations with nonloca…
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction…
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially…
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential $K$. We are interested in establishing their well-posedness theory when the nonlocal interaction potential $K$ is neither differentiable nor…
We investigate the long term behavior in terms of global attractors, as time goes to infinity, of solutions to a continuum model for biological aggregations in which individuals experience long-range social attraction and short range…
We investigate the confinement properties of solutions of the aggregation equation with repulsive-attractive potentials. We show that solutions remain compactly supported in a large fixed ball depending on the initial data and the…
We study the question of global attraction, in the energy norm, for finite energy solutions to classical particle coupled to a scalar wave field. The attraction could take place to either the set of the stationary solutions in the case of a…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
In this paper, we consider a damped Navier-Stokes-Bardina model posed on the whole three-dimensional. These equations have an important physical motivation and they arise from some oceanic model. From the mathematical point of view, they…
We investigate the large time behavior of multi-dimensional aggregation equations driven by Newtonian repulsion, and balanced by radial attraction and confinement. In case of Newton repulsion with radial confinement we quantify the…
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…
We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and the classical (nonlinear) elastic plate equation for in-plane motions on a flexible flat part of the boundary. The…
We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…
In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and…
We study an aggregation PDE with competing attractive and repulsive forces on a sphere of arbitrary dimension. In particular, we consider the limit of strongly localized repulsion with a constant attraction term. We prove convergence of…
We consider a Nicholson's equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
The global attraction is proved for the nonlinear 3D Klein-Gordon equation with a nonlinearity concentrated at one point. Our main result is the convergence of each "finite energy solution" to the manifold of all solitary waves as…
We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one…
We study the multidimensional aggregation equation $u_t+\Div(uv)=0$, $v=-\nabla K*u$ with initial data in $\cP_2(\bR^d)\cap L_{p}(\bR^d)$. We prove that with biological relevant potential $K(x)=|x|$, the equation is ill-posed in the…
The global attraction is established for all finite energy solutions to a model $\mathbf{U}(1)$-invariant nonlinear Klein-Gordon equation in one dimension coupled to a finite number of nonlinear oscillators: We prove that {\it each finite…