Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

BLOW-UP IN A FRACTIONAL LAPLACIAN MUTUALISTIC MODEL WITH NEUMANN BOUNDARY CONDITIONS

In this paper,a fractional Laplacian mutualistic system under Neumann boundary conditions is studied.Using the method of upper and lower solutions,it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

This paper deals with the blow-up properties of solutions to semilinear heat equation ut-uxx= up in (0, 1) × (0, T) with the Neumann boundary condition ux(0, t) = 0, u:x1, t) = 1 on [0, T). The necessary and sufficient conditions under which all solutions to have a finite time blow-up and the exact blow-up rates are established. It is proved that the blow-up will occur only at the boundary x = 1. The asymptotic behavior near the blow-up time is also studied.

An extended iterative direct-forcing immersed boundary method in thermo-fluid problems with Dirichlet or Neumann boundary conditions

An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.

Neumann Boundary Conditions Inhibiting SSB in Coleman-Weinberg Mechanism

In this work we show that homogeneous Neumann boundary conditions inhibit the Coleman-Weinberg mechanism for spontaneous symmetry breaking in the scalar electrodynamics if the length of the finite region is small enough （a = e2Mφ-1, where M, is the mass of the scalar field generated by the Coleman-Weinberg mechanism）.

An extension result for the Landau-Lifshitz equation with Neumann boundary condition

We establish an extension result of existence and partial regularity for the nonzero Neumann initial-boundary value problem of the Landau-Lifshitz equation with nonpositive anisotropy constants in three or four dimension space. The partial regularity is proved up to the boundary and this result is an important supplement to those for the Dirichlet problem or the homogeneous Neumann problem.

Existence of Solutions for p-Laplace Equations Subjected to Neumann Boundary Value Problem

The existence of solutions for one dimensional p-Laplace equation （φp（u′））′=f（t,u,u′） with t∈（0,1） and Фp（s）=｜s｜^p-2 s, s≠0 subjected to Neumann boundary value problem at u′（0） = 0, u′（1） = 0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.

Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems

Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L2 (Γ) and L∞ (Γ) norm. For state and adjoint state, optimal convergence order in the L2 (Ω) and H1 (Ω) can also be obtained.

Numerical analysis of a Neumann boundary control problem with a stochastic parabolic equation

We analyze the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where additive noise occurs in the Neumann boundary condition. The convergence is established for general filtration, and the convergence rate O(τ1/4-?+ h1/2-?) is derived for the natural filtration of the Q-Wiener process.

Lipschitz Continuity and Explicit Form of Solution in a Class of Free Boundary Problem with Neumann Boundary Condition

We consider a class of free boundary problems with Neumann boundary conditions.We would like to give certain results with regularity of solutions(mainly the local interior and boundary Lipschitz continuity).We will also show an explicit form of solution under well-specified conditions.

The Blow-up Rate for a System of Heat Equations with Neumann Boundary Conditions

This paper deals with the blow-up properties of solutions to a system of heat equations u_t=Δ_u,v_t=Δv in B_R×(0,T) with the Neumann boundary conditions u/η=e^v,v/η=e^u on S_R×[0,T).The exact blow-up rates are established.It is also proved that the blow-up will occur only on the boundary.

Exact Boundary Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls

In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.

Quenching Time for a Semilinear Heat Equation with a Nonlinear Neumann Boundary Condition

In this paper we consider the finite time quenching behavior of solutions to a semilinear heat equation with a nonlinear Neumann boundary condition. Firstly, we establish conditions on nonlinear source and boundary to guarantee that the solution doesn＇t quench for all time. Secondly, we give sufficient conditions on data such that the solution quenches in finite time, and derive an upper bound of quenching time. Thirdly, undermore restrictive conditions, we obtain a lower bound of quenching time. Finally, we give the exact bounds of quenching time of a special example.

POSITIVE SOLUTIONS OF SINGULAR SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM

In this paper, we obtain the existence of positive solutions for singular second-order Neumann boundary value problem by using the fixed point indices, the result generalizes some present results.

POSITIVE SOLUTIONS TO FOURTH-ORDER NEUMANN BOUNDARY VALUE PROBLEM

In this paper, we study a class of fourth-order Neumann boundary value problem (NBVP for short). By virtue of fixed point index and the spectral theory of linear operators, the existence of positive solutions is obtained under the assumption that the nonlinearity satisfies sublinear or superlinear conditions, which are relevant to the first eigenvalue of the corresponding linear operator.

A NOTE ON THE SOLUTION TO NEUMANN BOUNDARY VALUE PROBLEM OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

The author of this paper, by means of the semi-rank theory, establish a new comparative theorem and give the existence of maximal and minimal solutions to Neumann boundary value problems of second order nonlinear differential equation in ordered Banach spaces when the upper and lower solutions in the reversed order of the problem are given.

Well-posedness for the Cahn-Hilliard Equation with Neumann Boundary Condition on the Half Space

In this paper, we investigate the Cahn-Hilliard equation defined on the half space and subject to the Neumann boundary and initial condition. For given initial data in some sobolev space, we prove the existence and analytic smoothing effect of the solution.

Lower Bound Estimate of Blow Up Time for the Porous Medium Equations under Dirichlet and Neumann Boundary Conditions

In this paper,we establish the lower bounds estimate of the blow up time for solutions to the nonlocal cross-coupled porous medium equations with nonlocal source terms under Dirichlet and Neumann boundary conditions.The results are obtained by using some differential inequality technique.

A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions

In this paper,we study a lattice Boltzmann method for the advectiondiffusion equation with Neumann boundary conditions on general boundaries.A novel mass conservative scheme is introduced for implementing such boundary conditions,and is analyzed both theoretically and numerically.Second order convergence is predicted by the theoretical analysis,and numerical investigations show that the convergence is at or close to the predicted rate.The numerical investigations include time-dependent problems and a steady-state diffusion problem for computation of effective diffusion coefficients.