A reaction-diffusion problem with a reaction front

A reaction-diffusion problem with a reaction front

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 no...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 21; no. 5; pp. 417 - 432
Main Author: Vannini, Endrio
Format: Journal Article
Language:English
Published: Stuttgart John Wiley & Sons, Ltd 25-03-1998
Wiley
Teubner
Subjects:
Exact sciences and technology
Function theory, analysis
Mathematical analysis
Mathematical methods in physics
Mathematics
Ordinary differential equations
Physics
Sciences and techniques of general use
Non linear equation
Solution uniqueness
Third order equation
Boundary value problem
One-dimensional calculations
Gas flow
Differential equation
Existence of solution
Numerical solution
Reaction diffusion equation
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Summary: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.
Bibliography:ark:/67375/WNG-0VX4V6NW-J
ArticleID:MMA959
istex:57A1DA1EDF782F4171A0E8BBE14656C116180834
ISSN:0170-4214
1099-1476
DOI:10.1002/(SICI)1099-1476(19980325)21:5<417::AID-MMA959>3.0.CO;2-9