Functional and Integral Equations for Strip Diffraction (Neumann Boundary Problem)

2013 ◽  
pp. 213-246
Keyword(s):  
Boundary Problem ◽  
Integral Equations ◽  
Neumann Boundary

scholarly journals ANALYSIS OF DIRECT SEGREGATED BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR VARIABLE-COEFFICIENT MIXED BVPs IN EXTERIOR DOMAINS

2013 ◽  
Vol 11 (04) ◽  
pp. 1350006 ◽  
Author(s):  
O. CHKADUA ◽  
S. E. MIKHAILOV ◽  
D. NATROSHVILI
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Variable Coefficient ◽  
Boundary Value ◽  
Weighted Sobolev Spaces ◽  
Elliptic Partial Differential Equation ◽  
Neumann Boundary ◽  
Infinite Domains ◽  
Domain Integral

Direct segregated systems of boundary-domain integral equations are formulated for the mixed (Dirichlet–Neumann) boundary value problems for a scalar second-order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding properties of the BVPs in weighted Sobolev spaces that are proved as well.

Decomposition of Plane Waves into Irreducible Representations of Space Groups

1995 ◽  
Vol 50 (6) ◽  
pp. 577-583
Author(s):  
H. Teuscher ◽  
P. Kramer
Keyword(s):  
Dirichlet Problem ◽  
Representation Theory ◽  
Boundary Problem ◽  
Plane Waves ◽  
Neumann Boundary ◽  
Basis Functions ◽  
Irreducible Representations ◽  
Space Groups ◽  
Crystallographic Space Groups ◽  
Representations Of Space

Abstract Using a relation between representation theory of crystallographic space groups and a Dirichlet type of boundary problem for the Laplacian, we derive the solutions for the Dirichlet problem, as well as for a similar Neumann boundary problem, by a complete decomposition of plane waves into irreducible representations of a particular space group. This decomposition corresponds to a basis transformation in L2(Ω) and yields a new set of basis functions adapted to the symmetry of the lattice considered.

scholarly journals ON THE DIRICHLET-NEUMANN BOUNDARY PROBLEM FOR SCALAR CONSERVATION LAWS

2016 ◽  
Vol 21 (5) ◽  
pp. 685-698
Author(s):  
Marin Mišur ◽  
Darko Mitrovic ◽  
Andrej Novak
Keyword(s):  
Approximate Solution ◽  
Conservation Laws ◽  
Boundary Problem ◽  
Neumann Boundary ◽  
Compensated Compactness ◽  
Scalar Conservation Laws ◽  
Basic Tool ◽  
Numerical Examples ◽  
Elliptic Approximation ◽  
Scalar Conservation

We consider a Dirichlet-Neumann boundary problem in a bounded domain for scalar conservation laws. We construct an approximate solution to the problem via an elliptic approximation for which, under appropriate assumptions, we prove that the corresponding limit satisfies the considered equation in the interior of the domain. The basic tool is the compensated compactness method. We also provide numerical examples.

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