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A reaction–diffusion problem with a reaction front
Author(s) -
Vannini Endrio
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19980325)21:5<417::aid-mma959>3.0.co;2-9
Subject(s) - mathematics , uniqueness , boundary value problem , ordinary differential equation , reaction–diffusion system , initial value problem , mathematical analysis , differential equation
Abstract We state a 1D model with quasi‐stationary gas flows approximation for a carbon reactivity test in the production of silicon. The mathematical problem we formulate is a non‐linear boundary value problem for a third‐order ordinary differential equation with non‐linear boundary conditions, which are non‐local in time. We prove existence and uniqueness of a classical solution and provide a numerical example. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.