Symmetric Solutions of a Nonlinear Elliptic Problem with Neumann Boundary Condition

The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition

Abstract. We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition −∂u/∂νA = g(·, ·, u) with a locally defined, Lr-bounded function g(t, ·, ξ). We prove the existence of a local weak solution to the problem by means of ...

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

A Spectral Method for an Elliptic Equation with a Nonlinear Neumann Boundary Condition

Abstract. Let Ω be an open, simply connected, and bounded region in Rd, d ≥ 2, that is diffeomorphic to Bd. Consider solving −∆u+ γu = 0 over Ω with the Neumann boundary condition ∂u ∂n = b (·, u). The function b is a nonlinear function of u. The problem is reformulated in a weak form, and then a spectral Galerkin method is used to create a sequence of finite dimensional nonlinear problems. An ...

Parallel Fictitious Domain Method for a Nonlinear Elliptic Neumann Boundary Value Problem Parallel Fictitious Domain Method for a Nonlinear Elliptic Neumann Boundary Value Problem

Parallelization of the algebraic ctitious domain method is considered for solving Neumann boundary value problems with variable coeecients. The resulting method is applied to the parallel solution of the subsonic full potential ow problem which is linearized by the Newton method. Good scalability of the method is demonstrated in Cray T3E distributed memory parallel computer using MPI in communi...

A Boundary Meshless Method for Neumann Problem

Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...