The existence of inertial manifolds for a Smoluchowski equation – a nonlinear Fokker-Planck equation on the unit sphere which arises in modeling of colloidal suspensions – is investigated. A nonlinear and nonlocal transformation is used to eliminate the gradient from the nonlinear term.

We summarize all the known properties of the supersymmetric integrable Two Boson equation. We present its nonstandard Lax formulation and tri-Hamiltonian structure, its reduction to the supersymmetric nonlinear Schrödinger equation and the local as well as nonlocal conserved charges. We also present the algebra of the conserved charges and identify its second Hamiltonian structure with the twis...

The existence of inertial manifolds for a Smoluchowski equation—a nonlinear and nonlocal Fokker–Planck equation which arises in the modelling of colloidal suspensions—is investigated. The difficulty due to first-order derivatives in the nonlinearity is circumvented by a transformation. Mathematics Subject Classification: 35Kxx, 70Kxx

The Cauchy problem for the Fokker–Plank–Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker–Plank– Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

We consider the stability of a finite difference scheme with two weight parameters for a hyperbolic equation with nonlocal integral boundary conditions. We obtain stability region in the complex plane by investigating the characteristic equation of a difference scheme using the root criterion.

|An explicit extrapolated box method is considered for a nonlinear partial integrodif-ferential equation, the Gurtin-MacCamy equation, subject to a nonlocal boundary condition. This problem describes the evolution in time of the age structure of a population. The consistency, stability and convergence properties of the method are studied, and its second order accuracy is demonstrated both analy...

A kinetic equation which combines the quasiparticle drift of Landau’s equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider’s equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary coll...

Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions b...

Abstract. In this paper we study the nonlocal p-Laplacian-type diffusion equation ut(t, x) = ∫ RN J(x−y)|u(t, y)−u(t, x)|p−2(u(t, y)−u(t, x)) dy, (t, x) ∈]0, T [×Ω, with u(t, x) = ψ(x) for (t, x) ∈ ]0, T [×(RN \Ω). If p > 1, this is the nonlocal analogous problem to the well-known local p-Laplacian evolution equation ut = div(|∇u|p−2∇u) with Dirichlet boundary condition u(t, x) = ψ(x) on (t, x)...