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Iterative bounds for the stable solutions of convex non-linear boundary value problems*

Published online by Cambridge University Press:  14 February 2012

J. W. Mooney  and
G. F. Roach
J. W. Mooney
Affiliation:
Paisley College of Technology
G. F. Roach
Affiliation:
University of Strathclyde
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Synopsis

We consider a class of convex non-linear boundary value problems of the form

where L is a linear, uniformly elliptic, self-adjoint differential expression, f is a given non-linear function, B is a boundary differential expression of either Dirichlet or Neumann type and D is a bounded open domain with boundary ∂D. Particular problems of this class arise in the process of thermal combustion [8].

In this paper we show that stable solutions of this class can be bounded from below (above) by a monotonically increasing (decreasing) sequence of Newton (Picard) iterates. The possibility of using these schemes to construct unstable solutions is also considered.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 2 , 1977 , pp. 81 - 94
Copyright
Copyright © Royal Society of Edinburgh 1977

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