相关论文: Graph-to-local limit for a multi-species nonlocal …

We study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our strategy relies on the variational structure of both…

We explore the dynamical behavior and energetic properties of a model of two species that interact nonlocally on finite graphs. The authors recently introduced the model in the context of nonquadratic Finslerian gradient flows on…

We study the evolution of a system of two species with nonlinear mobility and nonlocal interactions on a graph whose vertices are given by an arbitrary, positive measure. To this end, we extend a recently introduced $2$-Wasserstein-type…

We consider dynamics driven by interaction energies on graphs. We introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with respect to a graph Wasserstein distance. The particular…

Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…

We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…

We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an…

We introduce nonlocal dynamics on directed networks through the construction of a fractional version of a nonsymmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both…

We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications.…

We deal with a nonlocal interaction equation describing the evolution of a particle density under the effect of a general symmetric pairwise interaction potential, not necessarily in convolution form. We describe the case of a convex (or…

We consider a nonlocal evolution equation representing the continuum limit of a large ensemble of interacting particles on graphs forced by noise. The two principle ingredients of the continuum model are a nonlocal term and Q-Wiener process…

We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…

We consider interacting particle systems with unbounded interaction range on general countably infinite graphs $S$ and prove explicit non-asymptotic error bounds for approximations of the infinite-volume dynamics by systems of finitely many…

We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic…

We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the…

Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…

We address a system of weakly interacting particles where the heterogenous connections among the particles are described by a graph sequence and the number of particles grows to infinity. Our results extend the existing law of large numbers…

We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential equations. The nonlocal equations are obtained as gradient flows of interaction-like energies…

We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…

We study a system of two continuity equations with nonlocal velocity fields using interaction potentials of both attractive and repulsive Morse type. Such a system is of interest in many contexts in multi-population modelling. We prove…