Digression on Generalizations of the Geometric Method of Solution. — Solutions of Equation (1.1) for the Domain x > 0 with a Boundary Condition at x = 0

1974 ◽  
pp. 21-34
Author(s):  
J. M. Burgers
Keyword(s):  
Boundary Condition ◽  
Geometric Method ◽  
Method Of Solution

On the Solution of Linear Diffusion Problems With Variable Boundary Condition Parameters

1974 ◽  
Vol 96 (1) ◽  
pp. 48-51 ◽  
Author(s):  
M. Necati O¨zis¸ik ◽  
R. L. Murray
Keyword(s):  
Boundary Condition ◽  
Cross Sections ◽  
Diffusion Theory ◽  
Transient Heat Conduction ◽  
Linear Diffusion ◽  
Variable Boundary ◽  
Absorbing Boundaries ◽  
Method Of Solution ◽  
Finite Medium ◽  
Type Boundary

A method of solution is presented for the treatment of a class of boundary value problems of linear diffusion theory for finite homogeneous media which have applications in transient heat conduction (or mass diffusion) in a finite medium subjected to convective type boundary condition with time and space dependent coefficient, in the processes of neutron slowing in a finite medium with absorbing boundaries that exhibit energy-dependent cross sections, and in many related areas.

scholarly journals First order differential systems with a nonlinear boundary condition via the method of solution-regions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Marlène Frigon ◽  
Marcos Tella ◽  
F. Adrián F. Tojo
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nonlinear Boundary Conditions ◽  
Linear Case ◽  
Differential Systems ◽  
First Order ◽  
Method Of Solution

AbstractIn this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear case.

One-Dimensional Fin-Tip Boundary Condition Correction II

2001 ◽  
Vol 22 (5) ◽  
pp. 35-40 ◽  
Author(s):  
D. C. Look Jr ◽  
Arvind Krishnan
Keyword(s):  
Boundary Condition ◽  
One Dimensional

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.

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