Finite-difference approximations to an elliptic–hyperbolic system arising in vortex density models for type II superconductors are studied. The problem can be formulated as a non-local Hamilton–Jacobi equation on a bounded domain with zero Neumann boundary conditions. Monotone schemes are defined and shown to be stable. An L∞ error bound is proved for the approximations of the unique viscosity ...

We study the heat content asymptotics on a Riemannian manifold with smoooth boundary defined by Dirichlet, Neumann, transmittal and transmission boundary conditions. Subject Classification: 58J50

This research is a natural continuation of the recent paper “Exact solutions of the simplified Keller–Segel model” (Commun Nonlinear Sci Numer Simulat 2013, 18, 2960–2971). It is shown that a (1+2)-dimensional Keller–Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible maximal algebras of invariance of the Neumann boundary value problems based on the Keller...

We deal with eigenvalue problems for the Laplacian varying mixed boundary conditions, consisting in homogeneous Neumann conditions on a vanishing portion of and Dirichlet complement. By study an Almgren-type frequency function, we derive upper lower bounds variation sharp estimates case strictly star-shaped region.

We prove comparison results between viscosity sub and supersolutions of degenerate elliptic and parabolic equations associated to, possibly non-linear, Neumann boundary conditions. These results are obtained under more general assumptions on the equation (in particular the dependence in the gradient of the solution) and they allow applications to quasilinear, possibly singular, elliptic or para...

Non-local boundary conditions for Euclidean quantum gravity are proposed, consisting of an integro-differential boundary operator acting on metric perturbations. In this case, the operator P on metric perturbations is of Laplace type, subject to non-local boundary conditions; by contrast, its adjoint is the sum of a Laplacian and of a singular Green operator, subject to local boundary condition...

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.

In this paper, we give a systematic study of the boundary layer behavior for linear convection-diffusion equation in the zero viscosity limit. We analyze the boundary layer structures in the viscous solution and derive the boundary condition satisfied by the viscosity limit as a solution of the inviscid equation. The results confirm that the Neumann type of far-field boundary condition is prefe...

In this paper we shall study the evolution of the zero set of the solution of the heat equation perturbed by a potential c and Neumann boundary conditions in one and two dimensions. 1. Introduction Let IR d be a bounded connected domain with a smooth boundary @ (we assume throughout that is of class C 3) and let c be a continuous function on , the closure of. Consider the heat equation with a p...

Immersed boundary methods are efficient tools of growing interest as they allow to use generic CFD codes to deal with complex, moving and deformable geometries, for a reasonable computational cost compared to classical bodyconformal or unstructured mesh approaches. In this work, we propose a new immersed boundary method based on a radial basis functions framework for the spreading-interpolation...