Study of an elliptic problem with nonlinear boundary conditions | Zendy

Caussignac Ph. | Zendy; Descloux J. | Zendy; Rappaz J. | Zendy; Nedelec J. C. | Zendy

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Study of an elliptic problem with nonlinear boundary conditions

Author(s) -

Caussignac Ph.,

Descloux 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.

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