G. R. Shendge

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Technical Report 202


One of the powerful methods of proving the existence of extremal solutions of initial and boundary value problems is the monotone iterative technique [1-4,6,7]. This has recently been applied [5] to a rather special type of boundary value problem [see pdf for notation] because, particular cases of (*) represent equations arising in the transport process of different types of particles moving in opposite directions, which are subjected to certain fluxes [8]. However (*) does not include situations in which the initial and final fluxes in a certain direction coincide. To cover this situation one needs to study a typical periodic boundary value problem (PBVP). This is precisely what we plan to consider in this paper. Developing a monotone technique for such a problem depends very much upon establishing a suitable comparison result. Hence we prove first an appropriate comparison result and then use it to develop a monotone technique for a PBVP, particular cases of which represent periodic transport processes. For transport processes arising in various physical situations, we refer to [7-9].


Mathematics | Physical Sciences and Mathematics

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Mathematics Commons



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