In Randall-Sundrum-type brane-world cosmologies, the dynamical equations on the three-brane differ from the general relativity equations by terms that carry the effects of imbedding and of the free gravitational field in the fivedimensional bulk. Instead of starting from an ansatz for the metric, we derive the covariant nonlinear dynamical equations for the gravitational and matter fields on th...

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

A deformation of the wave equation on a two-dimensional black hole is considered as a toy-model for possible gravitational or stringy nonlocal effects. The deformed wave-equation allows for an initial-value problem despite being nonlocal. The singularity present in the classical geometry is resolved by the deformation, so that propagation of a wave-packet can be continued through the classicall...

For the third order differential equation, y′′′ = f(x, y, y′, y′′), we consider uniqueness implies existence results for solutions satisfying the nonlocal 4-point boundary conditions, y(x1) = y1, y(x2) = y2, y(x3)− y(x4) = y3. Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal 3-point boundary condit...

Using our previous work on reflectionless analytic difference operators and a nonlocal Toda equation, we introduce analytic versions of the Volterra and Kac-van Moerbeke lattice equations. The real-valued N -soliton solutions to our nonlocal equations correspond to self-adjoint reflectionless analytic difference operators with N bound states. A suitable scaling limit gives rise to the N -solito...

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evo...

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the ga...