相关论文: Nonlocal to local convergence of phase field syste…
We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a…
In this paper, the long-time asymptotic behaviours of nonlocal porous medium equations with absorption or convection are studied. In the parameter regimes when the nonlocal diffusion is dominant, the entropy method is adapted in this…
The aim of this article is to develop the regularity theory for parabolic equations driven by nonlocal operators associated with nonsymmetric forms. H\"older regularity and weak Harnack inequalities are proved using extensions of recently…
In this paper, we are concerned with a quasi-linear hyperbolic-parabolic system of persistence and endogenous chemotaxis modelling vasculogenesis in $\mathbb{R}$. Under some suitable structural assumption on the pressure function, we first…
We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in the case of a W^{1,1} convolution kernel and under homogeneous Neumann conditions. Any type of potential,…
We present a scheme allowing to access the squeezing parameter of multimode fields by means of the dynamics of nonlocal quantum probes. The model under consideration is composed of two two-level systems which are coupled locally to an…
Many nonlocal models have adopted Euclidean balls as the nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal approximations of such balls. A crucial question is, to what extent…
In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band-edges. This goal is achieved by applying a diagrammatic…
This work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic-elliptic system…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
We propose a nonlocal theory of single-particle excitations. It is based on an off-diagonal effective medium and the projection operator method for treating the retarded Green function. The theory determines the nonlocal effective medium…
While temperature is well understood as an intensive quantity in standard thermodynamics, it is less clear whether the same holds in the presence of strong correlations, especially in the case of quantum systems, which may even display…
We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy…
We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground-state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian…
We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration of temperature, and phase parameter. The system is a…
We consider lattice gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas…
Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and…
In this note we investigate local properties for microlocally symmetrizable hyperbolic systems with just time dependent coefficients. Thanks to Paley-Wiener theorem, we establish finite propagation speed by showing precise estimates on the…
We analyze a family of non-local integral functionals of convolution-type depending on two small positive parameters $\varepsilon,\delta$: the first rules the length-scale of the non-local interactions and produces a `localization' effect…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…