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dc.contributor.author | Pachpatte, B. G. | en |
dc.contributor.author | Lakshmikantham, V. | en |
dc.date.accessioned | 2010-06-09T14:45:34Z | en |
dc.date.available | 2010-06-09T14:45:34Z | en |
dc.date.issued | 1981-04 | en |
dc.identifier.uri | http://hdl.handle.net/10106/2416 | en |
dc.description.abstract | **Please note that the full text is embargoed** ABSTRACT: Recently, monotone iterative methods have been successfully employed to prove existence of multiple solutions and point-wise bounds on solutions
of nonlinear boundary value problems for both ordinary and partial differential equations (see, [1], [3]-[6], [9]). In the transport process [10] of n different
types of particles in a finite rod of length (b-a) the equation governing the particle's density is given by the following linear system of equations
[see pdf for notation]
where Ai, Bi (i = 0,1,2) are n x n matrices and x,y,p,q are n-vectors. The components x1,...,xn of the vector x represent the n distinct type of particles moving in the forward direction along the rod while the componants
y1,...,yn of y are the ones moving in the backward direction. When the end of the rod are subjected to incident fluxes, the boundary conditions becomes
[see pdf for notation]
where the vectors xa, yb are given. Physical reasons demand that A0,B0
are diagonal matrices and all the elements in the matrices Ai, Bi (i = 0,1,2) are nonnegative functions on [a,b]. This specific boundary value problem then investigated by the method of successive approximations in [2,8] and by monotone method in [7]. Because of the importance of this problem in other physical applications, we extend in this paper the monotone technique to a general class of nonlinear boundary value problem which includes the tre”-;, problem treated in [2,7] as a special case. | en |
dc.language.iso | en_US | en |
dc.publisher | University of Texas at Arlington | en |
dc.relation.ispartofseries | Technical Report;159 | en |
dc.subject | Nonlinear boundary value problems | en |
dc.subject | Monotone method | en |
dc.subject | Transport processes | en |
dc.subject | Nonlinear boundary value problems | en |
dc.subject | BVP | en |
dc.subject.lcsh | Mathematical physics | en |
dc.subject.lcsh | Mathematics Research | en |
dc.title | Monotone Method for Nonlinear Boundary Value Problems Arising in Transport Process | en |
dc.type | Technical Report | en |
dc.publisher.department | Department of Mathematics | en |
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