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SOLUTION BRANCHES FOR NON-LINEAR EQUILIBRIUM PROBLEMS - BIFURCATION AND DOMAIN PERTURBATIONS

Abstract:

Consider the following simple, but typical, example of a non-linear equilibrium (differential equation) problem:. Δu = -λf(u) for (x, y) j{cyrillic, ukrainian} D,u = 0 for (x, y) j{cyrillic, ukrainian} D.Usually the eigenvalues of the (small u) linearized problem are simple, and each simple eigen value generates two solution branches for the full problem. However, the full problem nearly always has many other solution branches, and this paper describes how to find these other branches and why...

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Publication status:
Published

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Publisher copy:
10.1093/imamat/28.2.109

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
IMA JOURNAL OF APPLIED MATHEMATICS
Volume:
28
Issue:
2
Pages:
109-129
Publication date:
1982-01-01
DOI:
EISSN:
1464-3634
ISSN:
0272-4960
URN:
uuid:1e5d3a61-1f9e-47d1-8de5-db89734a34fb
Source identifiers:
10625
Local pid:
pubs:10625
Language:
English

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