In this paper, we study solutions to a nonlocal 1-Laplacian equation given by − ∫ ΩJ J(x− y) uψ(y)− u(x) |uψ(y)− u(x)| dy = 0 for x ∈ Ω, with u(x) = ψ(x) for x ∈ ΩJ \ Ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J . We also show that solutions in the...

We study the semilinear nonlocal equation ut = J∗u− u− u in the whole R . First, we prove the global well-posedness for initial conditions u(x, 0) = u0(x) ∈ L(R ) ∩ L∞(RN ). Next, we obtain the long time behavior of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J : finite time extinction for p < 1, faster than exponential decay for the ...

thin films of binary bi 0 -teo and bi 0 -v 0 systems were prepared by the thermal co-evaporation technique in a vacuum at room temperature. the optical absorption edge of these systems are studied in the wavelength of 200-800 nm using a perkin-elmer uv/vis spectrophotometer. it is found that the value of n=3/2 in the davis-mott equation is best fitted for the fundamental absorption edge for the...

This paper is concerned with a class of nonlocal dispersive models – the θ-equation proposed by H. Liu [ On discreteness of the Hopf equation, Acta Math. Appl. Sin. Engl. Ser. 24(3)(2008)423–440]: (1− ∂ x)ut + (1− θ∂ x) ( u2 2 ) x = (1− 4θ) ( ux 2 )

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...