Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Castro, L.P., and Kapanadze, D.. "Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions." Fractional Calculus and Applied Analysis 11.1 (2008): 15-26. <http://eudml.org/doc/11302>.

@article{Castro2008,
abstract = {Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness of the problem is obtained for a set of impedance parameters, and in a framework of Bessel potential spaces.∗ This work is partially supported by the Portuguese Science Foundation (FCT–Fundação para a Ciência ea Tecnologia) through Unidade de Investigação Matemática e Aplicações of the University of Aveiro, Portugal. * The second author is supported by the Portuguese Science Foundation through grant number SFRH/BPD/20524/2004.},
author = {Castro, L.P., Kapanadze, D.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {35J05; 35J25; 35C15; 47H50; 47G30},
language = {eng},
number = {1},
pages = {15-26},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions},
url = {http://eudml.org/doc/11302},
volume = {11},
year = {2008},
}

TY - JOUR
AU - Castro, L.P.
AU - Kapanadze, D.
TI - Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions
JO - Fractional Calculus and Applied Analysis
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 11
IS - 1
SP - 15
EP - 26
AB - Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness of the problem is obtained for a set of impedance parameters, and in a framework of Bessel potential spaces.∗ This work is partially supported by the Portuguese Science Foundation (FCT–Fundação para a Ciência ea Tecnologia) through Unidade de Investigação Matemática e Aplicações of the University of Aveiro, Portugal. * The second author is supported by the Portuguese Science Foundation through grant number SFRH/BPD/20524/2004.
LA - eng
KW - 35J05; 35J25; 35C15; 47H50; 47G30
UR - http://eudml.org/doc/11302
ER -