Asymptotic analysis for the eikonal equation with the dynamical boundary conditions

Numerical Boundary Conditions for the Fast Sweeping High Order WENO Methods for Solving the Eikonal Equation

High order fast sweeping methods have been developed recently in the literature to solve static Hamilton-Jacobi equations efficiently. Comparing with the first order fast sweeping methods, the high order fast sweeping methods are more accurate, but they often require additional numerical boundary treatment for several grid points near the boundary because of the wider numerical stencil. It is p...

Asymptotic analysis of the Gunn effect with realistic boundary conditions

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or ...

Wave equation with second–order non–standard dynamical boundary conditions

The paper deals with the well–posedness of the problem 8 >< >: utt −∆u = 0 in R× Ω, utt = kuν on R× Γ, u(0, x) = u0(x), ut(0, x) = v0(x) in Ω, where u = u(t, x), t ∈ R, x ∈ Ω, ∆ = ∆x denotes the Laplacian operator respect to the space variable, Ω is a bounded regular (C∞) open domain of RN (N ≥ 1), Γ = ∂Ω, ν is the outward normal to Ω, k is a constant. We prove that it is ill–posed if N ≥ 2, wh...

Maximal Regularity and Asymptotic Behavior of Solutions for the Cahn-Hilliard Equation with Dynamic Boundary Conditions

On the Numerical Solution of One Dimensional Schrodinger Equation with Boundary Conditions Involving Fractional Differential Operators

In this paper we study of collocation method with Radial Basis Function to solve one dimensional time dependent Schrodinger equation in an unbounded domain. To this end, we introduce artificial boundaries and reduce the original problem to an initial boundary value problem in a bounded domain with transparent boundary conditions that involves half order fractional derivative in t. Then in three...