scholarly journals Analysis of the Fully Developed Chute Flow of Granular Materials

1992 ◽  
Vol 59 (1) ◽  
pp. 109-119 ◽  
Author(s):  
Hojin Ahn ◽  
Christopher E. Brennen ◽  
Rolf H. Sabersky
Keyword(s):  
Boundary Value Problem ◽  
Granular Materials ◽  
Solid Fraction ◽  
Shooting Method ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Granular Temperature ◽  
Mean Velocity ◽  
Chute Flow ◽  
Two Parameters

Existing constitutive relations and governing equations have been used to solve for fully developed chute flows of granular materials. In particular, the results of Lun et al. (1984) have been employed and the boundary value problem has been formulated with two parameters (the coefficient of restitution between particles, and the chute inclination), and three boundary values at the chute base wall, namely the values of solid fraction, granular temperature, and mean velocity at the wall. The boundary value problem has been numerically solved by the “shooting method.” The results show the significant role played by granular conduction in determining the profiles of granular temperature, solid fraction, and mean velocity in chute flows. These analytical results are also compared with experimental measurements of velocity fluctuation, solid fraction, and mean velocity made by Ahn et al. (1989), and with the computer simulations by Campbell and Brennen (1985b).

A two point boundary value problem for neutral functional differential equations

1983 ◽  
Vol 94 (3-4) ◽  
pp. 331-338
Author(s):  
Y. G. Sficas ◽  
S. K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Shooting Method ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Point Boundary ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Image Position

SynopsisThis paper is concerned with the existence of solutions of a two point boundary value problem for neutral functional differential equations. We consider the problemwhere M and N are n × n matrices. This is examined by using the “shooting method”. Also, an example is given to illustrate how our result can be applied to yield the existence of solutions of a periodic boundary value problem.

scholarly journals NONLOCAL THIRD ORDER BOUNDARY VALUE PROBLEMS WITH SOLUTIONS THAT CHANGE SIGN

2014 ◽  
Vol 19 (2) ◽  
pp. 145-154
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Shooting Method ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Scaling Method ◽  
Number Of Solutions

We investigate the existence and the number of solutions for a third order boundary value problem with nonlocal boundary conditions in connection with the oscillatory behavior of solutions. The combination of the shooting method and scaling method is used in the proofs of our main results. Examples are included to illustrate the results.

Existence and uniqueness for two-point boundary value problems

1981 ◽  
Vol 88 (3-4) ◽  
pp. 219-234 ◽  
Author(s):  
John V. Baxley ◽  
Sarah E. Brown
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Point Boundary ◽  
Initial Value

SynopsisBoundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

scholarly journals A boundary value problem of elastoplastic deformation process theory: Existence and uniqueness theorems

1994 ◽  
Vol 35 (4) ◽  
pp. 506-524
Author(s):  
Dao Huy Bich
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Deformation Process ◽  
Elastoplastic Deformation ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Complex Loading ◽  
Process Theory ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems

AbstractThis paper deals with the complete constitutive relations of elastoplastic deformation process theory, based on llyushin's postulate of isotropy and hypotheses of local determinancy and complanarity in plastic stage with complex loading. The formulation of the boundary value problem is given and existence and uniqueness theorems are considered.

scholarly journals Positive Solutions for a Second-Orderp-Laplacian Boundary Value Problem with Impulsive Effects and Two Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Meiqiang Feng
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Impulsive Effects ◽  
Upper And Lower Bounds ◽  
Existence And Multiplicity ◽  
Impulsive Boundary Value Problem ◽  
General Existence ◽  
The One ◽  
Two Parameters

The author considers an impulsive boundary value problem involving the one-dimensionalp-Laplacian-(φp (u′))′=λωtft,u,  0<t<1,  t≠tk,  Δu|t=tk=μIktk,  utk,  Δu′|t=tk=0,  k=1,2,…,n,  au(0)-bu′(0)=∫01‍g(t)u(t)dt,u′(1)=0, whereλ>0andμ>0are two parameters. Using fixed point theories, several new and more general existence and multiplicity results are derived in terms of different values ofλ>0andμ>0. The exact upper and lower bounds for these positive solutions are also given. Moreover, the approach to deal with the impulsive term is different from earlier approaches. In this paper, our results cover equations without impulsive effects and are compared with some recent results by Ding and Wang.

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