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The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
The regularity estimates have well-established for second-order elliptic and parabolic equations, as well as for equations with stable-like non-local operators. Whether similar results hold for non-lo...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to th...
We prove the existence and give the asymptotic behavior of non local fronts in homogeneous media.
We consider the Fisher-KPP equation with a nonlocal saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher-KPP equation. Our fir...
The paper is devoted to the proof of the uniqueness theorem for solution of the equation for the non-local ionization source in a glow discharge and a hollow cathode in general 3D geometry. The theore...
Abstract: We consider, in a $D-$dimensional cylinder, a non--local evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki...
We consider nonlocal linear Schr¨odinger-type critical systems of the type 1/4v = v in IR. (1) where is antisymmetric potential in L2(IR, so(m)), v is a IRm valued map and v denotes the matrix mu...
In this paper we prove the global in time well-posedness of the following non-local diffusion equation with ∈ [0, 2/3):@tu = (−△)−1u △u + u2, u(t = 0) = u0.
We present a study of what may be called an intrinsic metric for a general regular Dirichlet form. For such forms we then prove a Rademacher type theorem.
The ageing algebra is a local dynamical symmetry of many ageing systems, far from equilibrium, and with a dynamical exponent z=2. Here, new representations for an integer dynamical exponent z=n are co...
A review of non-local, deep transport mechanisms in the atmosphere of Earth provides a good foundation for examining whether similar mechanisms are operating in the atmospheres of Mars and Titan. On E...
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hi...
Motivated by the "tug-of-war" game studied in [12], we consider a "non-local" version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of f...

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