We consider some elliptic boundary value problems in a self-similar ramified domain of R with a fractal boundary with Laplace’s equation and nonhomogeneous Neumann boundary conditions. The Hausdorff dimension of the fractal boundary is greater than one. The goal is twofold: first rigorously define the boundary value problems, second approximate the restriction of the solutions to subdomains obt...

We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x, u, ux) on the unit interval 0 ≤ x ≤ 1 with Neumann boundary conditions. A permutation πf is defined by the two orderings of the set of (hyperbolic) equilibrium solutions ut ≡ 0 according to their respective values at the two boundary points x = 0 and x = 1. We prove that two global attractors, Af and Ag, are glo...

Abstract We consider an inverse boundary value problem for a semilinear wave equation on time-dependent Lorentzian manifold with time-like boundary. The coefficients of the nonlinear terms can be recovered in interior from knowledge Neumann-to-Dirichlet map. Either distorted plane waves or Gaussian beams used to derive uniqueness.

In this paper, a hybrid approach for solving the Laplace equation in general threedimensional (3-D) domains is presented. The approach is based on a local method for the Dirichletto-Neumann (DtN) mapping of a Laplace equation by combining a deterministic (local) boundary integral equation (BIE) method and the probabilistic Feynman–Kac formula for solutions of elliptic partial differential equat...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic B-splines as weight functions has been developed to solve a general seventh order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and ...

In this paper we consider 2D nonlocal diffusion models with a finite horizon parameter δ characterizing the range of interactions, and treatment Neumann-like boundary conditions that have proven challenging for discretizations models. We propose new generalization classical local Neumann by converting flux to correction term in model, which provides an estimate interactions each point points ou...

This paper deals with a finite element method involving Petrov-Galerkin method with quartic B-splines as basis functions and sextic B-splines as weight functions to solve a general sixth order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and Neumann type ...

In this paper, we prove long time existence and convergence results for a class of general curvature flows with Neumann boundary condition. This is the first result for the Neumann boundary problem of non Monge-Ampere type curvature equations. Our method also works for the corresponding elliptic setting.