On Sensitive Vector Poisson and Stokes Problems

1997 ◽  
Vol 07 (05) ◽  
pp. 681-698 ◽  
Author(s):  
J.-L. Guermond ◽  
L. Quartapelle
Keyword(s):  
Boundary Value Problems ◽  
Unique Solution ◽  
Poisson Equation ◽  
Bilinear Form ◽  
Variational Formulation ◽  
Biharmonic Equation ◽  
Stokes Problem ◽  
Boundary Value ◽  
Natural Conditions ◽  
Stokes Problems

Lions/Sanchez-Palencia's theory of sensitive boundary value problems is extended from the scalar biharmonic equation to the vector Poisson equation and the Stokes problem associated with the bilinear form (∇ × u, ∇ × v) + (∇ · u, ∇ · v). For both problems the specification of completely natural conditions for the vector unknown on a part of the boundary leads to a variational formulation admitting a unique solution which is however sensitive to abitrarily small smooth perturbations of the data, as shown in the present paper.

A new method for calculating eigenvalues with applications to gravity-capillary waves with edge constraints

1983 ◽  
Vol 94 (3) ◽  
pp. 553-564 ◽  
Author(s):  
James Graham-Eagle
Keyword(s):  
Boundary Value Problems ◽  
Variational Formulation ◽  
Boundary Value ◽  
Capillary Waves ◽  
Original Study ◽  
New Method ◽  
Linear Boundary ◽  
Hydrodynamic Problem ◽  
Alternative Means ◽  
Standard Linear

The method to be described provides an alternative means of dealing with certain non-standard linear boundary-value problems. It is developed in several applications to the theory of gravity-capillary waves. The analysis is based on a variational formulation of the hydrodynamic problem, being motivated by and extending the original study by Benjamin and Scott [3].

Screen type mixed boundary value problems for anisotropic pseudo-Maxwell’s equations

2016 ◽  
Vol 23 (4) ◽  
pp. 511-518
Author(s):  
Otar Chkadua ◽  
Roland Duduchava ◽  
David Kapanadze
Keyword(s):  
Boundary Value Problems ◽  
Unique Solvability ◽  
Bilinear Form ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Potential Method ◽  
Mixed Boundary Value Problems ◽  
Well Posed

AbstractWe investigate screen type mixed boundary value problems for anisotropic pseudo-Maxwell’s equations. We show that the problems with tangent traces are well posed in tangent Sobolev spaces. The unique solvability results are proven based on the potential method and coercivity result of Costabel on the bilinear form associated with pseudo-Maxwell’s equations.

scholarly journals On the solvability of the main boundary value problems for a nonlocal Poisson equation

2019 ◽  
Vol 43 (3) ◽  
pp. 1604-1625 ◽  
Author(s):  
Valery V. KARACHIK ◽  
Abdizhahan M. SARSENBI ◽  
Batirkhan K TURMETOV
Keyword(s):  
Boundary Value Problems ◽  
Poisson Equation ◽  
Boundary Value
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