scholarly journals Hypersingular nonlinear boundary-value problems with a small parameter

2018 ◽  
Vol 81 ◽  
pp. 93-98
Author(s):  
Andrei D. Polyanin ◽  
Inna K. Shingareva
Keyword(s):  
Small Parameter ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

scholarly journals On the Convergence of a Nonlinear Boundary-Value Problem in a Perforated Domain

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Yulia Koroleva
Keyword(s):  
Boundary Value Problem ◽  
Small Parameter ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Perforated Domain ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Convergence Of Solution

We consider a family with respect to a small parameter of nonlinear boundary-value problems as well as the corresponding spectral problems in a domain perforated periodically along a part of the boundary. We prove the convergence of solution of the original problems to the solution of the respective homogenized problem in this domain.

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