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Steady states of the reaction-diffusion equations. Part 1: Questions of existence and continuity of solution branches

Published online by Cambridge University Press:  17 February 2009

J. G. Burnell ,
A. A. Lacey  and
G. C. Wake
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Abstract

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When material is undergoing an exothermic chemical reaction which is sustained by the diffusion of a reactant, the steady-state regime is governed by a coupled pair of nonlinear elliptic partial differential equations with linear boundary conditions. In this paper we consider questions of existence of solutions to these equations. It is shown that, with the exception of the special case in which the mass-transfer is uninhibited on the boundary, a solution always exists, whereas in this special case a solution exists only for sufficiently low values of the exothermicity. Bounds are established for the solutions and the occurrence of minimal and maximal solutions is shown for some cases. Finally the behaviour of the solution set with respect to one of the parameters is studied.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 4 , April 1983 , pp. 374 - 391
Copyright
Copyright © Australian Mathematical Society 1983

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