In this paper, we establish a globally quantitative estimate of unique continuation at one time point for solutions parabolic equations with Neumann boundary conditions in bounded domains. Our proof is mainly based on Carleman commutator estimates and global frequency function argument, which motivated by recent work [5]. As an application, obtain observability inequality from measurable sets a...

This article follows the previous works [HKN] by Helffer-KleinNier and [HeNi1] by Helffer-Nier about the metastability in reversible diffusion processes via a Witten complex approach. Again, exponentially small eigenvalues of some self-adjoint realization of ∆ f,h = −h∆ + |∇f(x)| − h∆f(x) , are considered as the small parameter h > 0 goes to 0. The function f is assumed to be a Morse function o...

In this paper, a numerical scheme based on the three-dimensional block-pulse functions is proposed to solve the three-dimensional fractional Poisson type equations with Neumann boundary conditions. The differential operational matrices of fractional order of the three-dimensional block-pulse functions are derived from one-dimensional block-pulse functions, which are used to reduce the original ...

In this paper a finite element method involving Petrov-Galerkin method with quintic B-splines as basis functions and septic Bsplines as weight functions has been developed to solve a general eighth 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, the N...

The aim of this paper is twofold: On one hand we discuss an abstract approach to symmetrized Fredholm perturbation determinants and an associated trace formula for a pair of operators of positive-type, extending a classical trace formula. On the other hand, we continue a recent systematic study of boundary data maps, that is, 2× 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-...

In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.

We study the existence and uniqueness of solutions of the convective-diffusive elliptic equation −div(D∇u) + div(V u) = f posed in a bounded domain Ω ⊂ RN , with pure Neumann boundary conditions D∇u · n = (V · n)u on ∂Ω. Under the assumption that V ∈ Lp(Ω)N with p = N if N ≥ 3 (resp. p > 2 if N = 2), we prove that the problem has a solution u ∈ H1(Ω) if ∫ Ω f dx = 0, and also that the kernel is...

In this paper, the direct method is utilized for solving second order two-point boundary value problem of Neumann type. The method will obtain the solution of the second order boundary value problem directly without reducing it to to first order equations. The method will be implemented using variable step size via shooting technique adapted with the Newton method. Numerical results are given t...