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

Fractional Calculus and Applied Analysis (2008)

- Volume: 11, Issue: 1, page 15-26
- ISSN: 1311-0454

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topCastro, 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 -

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