scholarly journals A characterization of the eigenvalues of Schrödinger operators with Dirichlet and Neumann boundary conditions

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 657-658
Author(s):  
Jussi Behrndt ◽  
Jonathan Rohleder
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operators ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Schrodinger Operators

The eigenvalue gap for one-dimensional Schrödinger operators with symmetric potentials

2009 ◽  
Vol 139 (2) ◽  
pp. 359-366 ◽  
Author(s):  
Min-Jei Huang ◽  
Tzong-Mo Tsai
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operators ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Eigenvalue Gap

We consider the eigenvalue gap for Schrödinger operators on an interval with Dirichlet or Neumann boundary conditions. For a class of symmetric potentials, we prove that the gap between the two lowest eigenvalues is maximized when the potential is constant. We also give some related results for doubly symmetric potentials.

scholarly journals Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Martin Karuhanga
Keyword(s):  
Boundary Conditions ◽  
Bound States ◽  
Schrödinger Operators ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Schrodinger Operators ◽  
Eigenvalue Bounds ◽  
Negative Eigenvalues

This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L1 norms and Lln⁡L norms of the potential. Estimates involving the norms of the potential supported by a curve embedded in a strip are also presented.

scholarly journals Behavior of the -Laplacian on Thin Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Ricardo P. Silva
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
Thin Domains ◽  
Limiting Behavior

We give the characterization of the limiting behavior of solutions of elliptic equations driven by the -Laplacian operator with Neumann boundary conditions posed in a family of thin domains.

scholarly journals A concrete realization of the slow-fast alternative for a semilinear heat equation with homogeneous Neumann boundary conditions

2018 ◽  
Vol 7 (3) ◽  
pp. 375-384 ◽  
Author(s):  
Marina Ghisi ◽  
Massimo Gobbino ◽  
Alain Haraux
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Linear Part ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Semilinear Heat Equation ◽  
Codimension One ◽  
Concrete Realization

AbstractWe investigate the asymptotic behavior of solutions to a semilinear heat equation with homogeneous Neumann boundary conditions. It was recently shown that the nontrivial kernel of the linear part leads to the coexistence of fast solutions decaying to 0 exponentially (as time goes to infinity), and slow solutions decaying to 0 as negative powers of t. Here we provide a characterization of slow/fast solutions in terms of their sign, and we show that the set of initial data giving rise to fast solutions is a graph of codimension one in the phase space.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

scholarly journals Critique on “Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry”

2021 ◽  
Vol 433 ◽  
pp. 110163
Author(s):  
Ramakrishnan Thirumalaisamy ◽  
Nishant Nangia ◽  
Amneet Pal Singh Bhalla
Keyword(s):  
Boundary Conditions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Scalar Flux ◽  
Complicated Geometry

scholarly journals Radial positive solutions of elliptic systems with Neumann boundary conditions

2013 ◽  
Vol 265 (3) ◽  
pp. 375-398 ◽  
Author(s):  
Denis Bonheure ◽  
Enrico Serra ◽  
Paolo Tilli
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Neumann Boundary ◽  
Elliptic Systems ◽  
Neumann Boundary Conditions

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

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