This boundary condition is called as the Neumann boundary condition
, and it is widely applied to the thermal stress and temperature analysis of mass concrete [45, 46].
We consider the problems with homogeneous Neumann boundary condition
As pointed out by Dassios , the existence of the continuous one-dimensional distribution of images in the proposed image system is characteristic of the Neumann boundary condition
, which in fact was shown 70 years ago by Weiss who studied image systems through applications of Kelvin's transformation in electricity, magnetism, and hydrodynamics [17,18].
where [[GAMMA].sup.t.sub.D] denotes the spacetime boundary where the Dirichlet boundary condition is given, [[GAMMA].sup.t.sub.N]denotes the spacetime boundary where the Neumann boundary condition
is given, [bar.f] denotes the Dirichlet boundary condition in the spacetime domain, and [bar.w] denotes the Neumann boundary condition
in the spacetime domain.
A Neumann boundary condition
in the Laplace or Poisson equation imposes the constraint that the directional derivative of \phi is some value at some location.
For h=0, Robin boundary condition becomes Neumann boundary condition
The subscript H is to denote the Neumann boundary condition
on the boundary [partial derivative][OMEGA] and [partial derivative]S.
The corresponding Neumann boundary condition
can be expressed as:
Keywords: Global solvability, double-diffusive convection, Brinkman-Forchheimer equations, Neumann boundary condition
, Soret's coefficient.
Although if [alpha] = 0 is referred to as a Neumann boundary condition
, even with [alpha] = constant the solution is said to only be unique up to this additive constant.
In this paper we consider the boundary value problems (BVPs) with either the Dirichlet boundary condition or Neumann boundary condition
. Consider the systems of second-order BVPs of the form
where B = 1 represents the Dirichlet boundary condition; B = [partial derivative]/[partial derivative]n represents the Neumann boundary condition
. Applying Dirichlet and Neumann boundary conditions
, we obtained