We present a general method to obtain static anisotropic spherically symmetric solutions, satisfying a nonlocal equation of state, from known density profiles. This equation of state describes, at a given point, the components of the corresponding energy-momentum tensor not only as a function at that point, but as a functional throughout the enclosed configuration. In order to establish the phy...

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J ∗u−u+G ∗ (f(u))− f(u) in R, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equatio...

Acceleration-induced nonlocality and the corresponding Lorentz-invariant nonlocal field equations of accelerated systems in Minkowski spacetime are discussed. Under physically reasonable conditions, the nonlocal equation of motion of the field can be derived from a varia-tional principle of stationary action involving a nonlocal Lagrangian that is simply obtained by composing the local inertial...

Ergodicity for local and nonlocal stochastic singular p-Laplace equations is proven, without restriction on the spatial dimension and for all p ∈ [1, 2). This generalizes previous results from [Gess, Tölle; JMPA, 2014], [Liu, Tölle; ECP, 2011], [Liu; JEE, 2009]. In particular, the results include the multivalued case of the stochastic (nonlocal) total variation flow, which solves an open proble...

Two new integrable nonlocal Davey–Stewartson equations are introduced. These equations provide two-spatial dimensional analogues of the integrable, nonlocal nonlinear Schrö-dinger equation introduced in Ablowitz and Musslimani (2013 Phys. Rev. Lett. 110 064105). Furthermore, like the latter equation, they also possess a PT symmetry and, as it is well known, this symmetry is important for the ...

The nonlocal boundary value problem for Schrödinger equation in a Hilbert space is considered. The second-order of accuracy r-modified Crank-Nicolson difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability of these difference schemes is established. A numerical method is proposed for solving a one-dimensional nonlocal boundary value ...

The frequency equation of carbon-nanotube-based cantilever sensor with an attached mass is derived analytically using nonlocal elasticity theory. According to the equation, the relationship between the frequency shift of the sensor and the attached mass can be obtained. When the nonlocal effect is not taken into account, the variation of frequency shift with the attached mass on the sensor is c...

In this paper, inspired from the study on denoising, segmentation and reconstruction in image processing, and combining with the theories of two phase flows, we introduce one class of initial-boundary value problem of the Cahn-Hilliard equation with nonlocal terms. Then, by using the Schauder fixed point theorem, we obtain the existence of weak solutions to this initial boundary value problem f...

An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space Wm 2 (G) are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on L2(G), and defined for functions from the space Wm 2 (G) that satis...

Well-posedness results for the state-based peridynamic nonlocal continuum model of solid mechanics are established with the help of a nonlocal vector calculus. The peridynamic strain energy density for an elastic constitutively linear anisotropic heterogenous solid is expressed in terms of the field operators of that calculus, after which a variational principle for the equilibrium state is def...