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Monotone Method for Nonlinear Boundary Value Problems Arising in Transport Process

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Monotone Method for Nonlinear Boundary Value Problems Arising in Transport Process

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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 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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