Jaspers On Communicology: The Scission Point Boundary Condition of Existence and Existenz in advance

2021 ◽  
Author(s):  
Thaddeus Martin ◽  
Keyword(s):  
Boundary Condition ◽  
Point Boundary ◽  
Scission Point

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

A -Laplacian problem with a multi-point boundary condition

2004 ◽  
Vol 59 (3) ◽  
pp. 319-333 ◽  
Author(s):  
Marta García-Huidobro ◽  
Rául Manásevich ◽  
Ping Yan ◽  
Meirong Zhang
Keyword(s):  
Boundary Condition ◽  
Point Boundary

Solutions of second order multi-point boundary value problems

2008 ◽  
Vol 145 (2) ◽  
pp. 489-510 ◽  
Author(s):  
JOHN R. GRAEF ◽  
LINGJU KONG
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Linear Integral ◽  
The Relationship

AbstractWe consider classes of second order boundary value problems with a nonlinearity f(t, x) in the equations and subject to a multi-point boundary condition. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. The symmetry of solutions is also studied. Conditions are determined by the relationship between the behavior of the quotient f(t, x)/x for x near 0 and ∞ and the largest positive eigenvalue of a related linear integral operator. Our analysis mainly relies on the topological degree and fixed point index theories.

ON POSITIVE EIGENFUNCTIONS OF STURM-LIOUVILLE PROBLEM WITH NONLOCAL TWO‐POINT BOUNDARY CONDITION

2007 ◽  
Vol 12 (2) ◽  
pp. 215-226 ◽  
Author(s):  
Sigita Pečiulytė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Liouville Problem ◽  
Point Boundary ◽  
Existence Domain ◽  
Classical Boundary ◽  
Sturm Liouville ◽  
Necessary And Sufficient ◽  
Nonlocal Boundary Problem

Positive eigenvalues and corresponding eigenfunctions of the linear Sturm‐Liouville problem with one classical boundary condition and another nonlocal two‐point boundary condition are considered in this paper. Four cases of nonlocal two‐point boundary conditions are analysed. We get positive eigenfunctions existence domain for each case of these problems. This domain depends on the parameters of the nonlocal boundary problem and it gives necessary and sufficient conditions for existing positive eigenvalues with positive eigenfunctions.

scholarly journals A finite difference scheme for a fluid dynamic traffic flow model appended with two-point boundary condition

2012 ◽  
Vol 31 ◽  
pp. 43-52 ◽  
Author(s):  
MO Gani ◽  
MM Hossain ◽  
LS Andallah
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Difference Scheme ◽  
Traffic Flow ◽  
Finite Difference Scheme ◽  
Flow Model ◽  
Fluid Dynamic ◽  
Point Boundary ◽  
Traffic Flow Model ◽  
First Order

A fluid dynamic traffic flow model with a linear velocity-density closure relation is considered. The model reads as a quasi-linear first order hyperbolic partial differential equation (PDE) and in order to incorporate initial and boundary data the PDE is treated as an initial boundary value problem (IBVP). The derivation of a first order explicit finite difference scheme of the IBVP for two-point boundary condition is presented which is analogous to the well known Lax-Friedrichs scheme. The Lax-Friedrichs scheme for our model is not straight-forward to implement and one needs to employ a simultaneous physical constraint and stability condition. Therefore, a mathematical analysis is presented in order to establish the physical constraint and stability condition of the scheme. The finite difference scheme is implemented and the graphical presentation of numerical features of error estimation and rate of convergence is produced. Numerical simulation results verify some well understood qualitative behavior of traffic flow.DOI: http://dx.doi.org/10.3329/ganit.v31i0.10307GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 31 (2011) 43-52

scholarly journals Stability of detonation in a circular pipe with porous walls

2012 ◽  
Vol 370 (1960) ◽  
pp. 668-688 ◽  
Author(s):  
Carlos Chiquete ◽  
Anatoli Tumin
Keyword(s):  
Boundary Condition ◽  
Stability Problem ◽  
Temporal Stability ◽  
Porous Wall ◽  
Circular Pipe ◽  
Normal Velocity ◽  
Point Boundary ◽  
Acoustic Boundary Condition ◽  
Porous Walls ◽  
The Stability

A stability analysis is carried out taking into account slightly porous walls in an idealized detonation confined to a circular pipe. The analysis is carried out using the normal-mode approach and corrections are obtained to the underlying impenetrable wall case results to account for the effect of the slight porosity. The porous walls are modelled by an acoustic boundary condition for the perturbations linking the normal velocity and the pressure components and thus replacing the conventional no-penetration boundary condition at the wall. This new boundary condition necessarily complicates the derivation of the stability problem with respect to the impenetrable wall case. However, exploiting the expressly slight porosity, the modified temporal stability can be determined as a two-point boundary value problem similar to the case of a non-porous wall.

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