On Trefftz’ integral equation for the Bernoulli free boundary value problem

2016 ◽  
Vol 136 (2) ◽  
pp. 503-522 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Integral Equation ◽  
Free Boundary ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Free Boundary Value Problem ◽  
Bernoulli Free Boundary

Singular perturbation of a nonlinear problem with multiple solutions

1985 ◽  
Vol 100 (3-4) ◽  
pp. 327-341
Author(s):  
Anne-Marie Lefevere
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Critical Value ◽  
Free Boundary Value Problem ◽  
Singular Limits ◽  
Natural Extensions ◽  
Barrier Parameter

SynopsisA nonlinear boundary value problem (P) having positive parameters L and a is considered. We associate with it a family of perturbed problems () affected by the presence of a barrier parameter γ related to L and a. There is a critical value L*(a) of the parameter L such that for L >L*(a), (P) has no regular solution. Then some natural extensions of (P), solutions of a free boundary value problem, arise as singular limits of ().

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