scholarly journals Eigenvalues of the Truncated Helmholtz Solution Operator under Strong Trapping

2021 ◽  
Vol 53 (6) ◽  
pp. 6724-6770
Author(s):  
Jeffrey Galkowski ◽  
Pierre Marchand ◽  
Euan A. Spence
Keyword(s):  
Solution Operator

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

The solution operator in Wp(1) for systems of neutral type

1997 ◽  
Vol 29 (10) ◽  
pp. 1173-1195
Author(s):  
E.N. Chukwu ◽  
H.C. Simpson
Keyword(s):  
Neutral Type ◽  
Solution Operator

scholarly journals On the continuity of the solution operator to the wave map system

2003 ◽  
Vol 57 (3) ◽  
pp. 357-383 ◽  
Author(s):  
Piero D'Ancona ◽  
Vladimir Georgiev
Keyword(s):  
Solution Operator
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