Geodesic
Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions
Fractional calculus and applied analysis, Tome 11 (2008) no. 1, pp. 15-26.

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We 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.
Keywords: Pseudo-Differential Operator, Helmholtz Equation, Boundary-Value Problem, Wave Diffraction, Hankel Function, 35J05, 35J25, 35C15, 47H50, 47G30 
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     title = {Pseudo-Differential {Operators} in a {Wave} {Diffraction} {Problem} with {Impedance} {Conditions}},
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Castro, L.P.; Kapanadze, D. Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions. Fractional calculus and applied analysis, Tome 11 (2008) no. 1, pp. 15-26. http://geodesic.mathdoc.fr/item/FCAA_2008_11_1_a0/