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Study of an elliptic problem with nonlinear boundary conditions
Author(s) -
Caussignac Ph.,
Descloux J.,
Rappaz J.,
Rappaz J.,
Nedelec J. C.
Publication year - 1987
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/mma.1670090121
Subject(s) - mathematics , square (algebra) , harmonic function , mathematical analysis , nonlinear system , inverse , boundary (topology) , elliptic function , derivative (finance) , boundary value problem , inverse problem , function (biology) , geometry , physics , quantum mechanics , evolutionary biology , financial economics , economics , biology
We consider the problem of finding on a trapezium a harmonic function u the normal derivative of which is equal on one side to λ exp(u). We prove the existence of a solution branch (λ, u (λ)) with a turning point and, for the case of the square, the presence of bifurcations. The “inverse power” algorithm converges on a part of the branch.