scholarly journals A QUANTUM TRANSMITTING SCHRÖDINGER–POISSON SYSTEM

2004 ◽  
Vol 16 (03) ◽  
pp. 281-330 ◽  
Author(s):  
M. BARO ◽  
H.-CHR. KAISER ◽  
H. NEIDHARDT ◽  
J. REHBERG
Keyword(s):  
Boundary Conditions ◽  
Bounded Domain ◽  
Real Axis ◽  
A Priori Estimates ◽  
A Priori ◽  
Poisson System ◽  
Transparent Boundary Conditions ◽  
Bounded Interval ◽  
Zero Current ◽  
Priori Estimates

We study a stationary Schrödinger–Poisson system on a bounded interval of the real axis. The Schrödinger operator is defined on the bounded domain with transparent boundary conditions. This allows us to model a non-zero current through the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

ON AN OPEN TRANSIENT SCHRÖDINGER–POISSON SYSTEM

2005 ◽  
Vol 15 (05) ◽  
pp. 667-688 ◽  
Author(s):  
NAOUFEL BEN ABDALLAH ◽  
FLORIAN MÉHATS ◽  
OLIVIER PINAUD
Keyword(s):  
Boundary Conditions ◽  
Electrostatic Interaction ◽  
A Priori Estimates ◽  
A Priori ◽  
Wave Functions ◽  
Open Boundary ◽  
Poisson System ◽  
Open Boundary Conditions ◽  
Transient Transport ◽  
Priori Estimates

A mathematical model of quantum transient transport in dimension d=2, 3 is derived and analyzed. The model describes the evolution of electrons injected into the device by reservoirs having a stationary statistics. The electrostatic potential in the device is modified by electron presence through electrostatic interaction. The wave functions are computed in the device region and satisfy nonhomogeneous open boundary conditions at the device edges. A priori estimates are deduced from the "dissipative properties" of the boundary conditions and from the repulsive character of the electrostatic interaction.

scholarly journals Uniform a priori estimates for elliptic problems with impedance boundary conditions

2020 ◽  
Vol 19 (5) ◽  
pp. 2445-2471
Author(s):  
Théophile Chaumont-Frelet ◽  
◽  
Serge Nicaise ◽  
Jérôme Tomezyk ◽  
Keyword(s):  
Boundary Conditions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Priori Estimates

scholarly journals An Energy Inequality and Its Applications of Nonlocal Boundary Conditions of Mixed Problem for Singular Parabolic Equations in Nonclassical Function Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Moussa Zakari Djibibe ◽  
Kokou Tcharie ◽  
N. Iossifovich Yurchuk
Keyword(s):  
Boundary Conditions ◽  
Mixed Problem ◽  
A Priori Estimates ◽  
A Priori ◽  
Energy Inequality ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Function Spaces ◽  
Priori Estimates ◽  
Singular Parabolic Equations

The aim of this paper is to establish a priori estimates of the following nonlocal boundary conditions mixed problem for parabolic equation: ∂v/∂t-(a(t)/x2)(∂/∂x)(x2∂v/∂x)+b(x,t)v=g(x,t), v(x, 0)=ψ(x), 0≤x≤ℓ, v(ℓ, t)=E(t), 0≤t≤T, ∫0ℓx3v(x,t)dx=G(t), 0≤t≤ℓ. It is important to know that a priori estimates established in nonclassical function spaces is a necessary tool to prove the uniqueness of a strong solution of the studied problems.

scholarly journals A priori estimates for the Fractional p-Laplacian with nonlocal Neumann boundary conditions and applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Dimitri Mugnai ◽  
Kanishka Perera ◽  
Edoardo Proietti Lippi
Keyword(s):  
Boundary Conditions ◽  
Morse Theory ◽  
A Priori Estimates ◽  
A Priori ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Priori Estimates ◽  
Variational Tools

<p style='text-indent:20px;'>We first prove that solutions of fractional <i>p</i>-Laplacian problems with nonlocal Neumann boundary conditions are bounded and then we apply such a result to study some resonant problems by means of variational tools and Morse theory.</p>

scholarly journals A PROBLEM WITH DISPLACEMENTS IN THE BOUNDARY CONDITIONS

2017 ◽  
Vol 17 (8) ◽  
pp. 102-107
Author(s):  
E.A. Utkina
Keyword(s):  
Boundary Conditions ◽  
Unknown Function ◽  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Fredholm Equations ◽  
Priori Estimates ◽  
Linear Hyperbolic Equations

A problem with conditions relating to the values of an unknown function on the opposite sides of a rectangular characteristiс domain D for a linear hyperbolic equations is considered. This problem is reduced to the system of Fredholm equations of the second kind. The proof of solvability is based on the a priori estimates of additional conditions on the coefficients of the equation.

scholarly journals ABSORBING BOUNDARY CONDITIONS FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH AN EXTERIOR POTENTIAL PART I: CONSTRUCTION AND A PRIORI ESTIMATES

2012 ◽  
Vol 22 (10) ◽  
pp. 1250026 ◽  
Author(s):  
XAVIER ANTOINE ◽  
CHRISTOPHE BESSE ◽  
PAULINE KLEIN
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
A Priori Estimates ◽  
Pseudodifferential Operators ◽  
A Priori ◽  
Absorbing Boundary Conditions ◽  
Two Dimensional ◽  
Absorbing Boundary ◽  
Priori Estimates

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.

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