Analytical inversion of the operator matrix for the problem of diffraction by a cylindrical segment in Sobolev spaces. (English. Russian original) Zbl 1467.45018
Comput. Math. Math. Phys. 61, No. 3, 424-430 (2021); translation from Zh. Vychisl. Mat. Mat. Fiz. 61, No. 3, 450-456 (2021).
Summary: A vector problem of electromagnetic-wave diffraction by a cylinder is described by a system of two two-dimensional integro-differential equations. After expanding the unknown functions and the right-hand sides in Fourier series, the problem reduces to systems of one-dimensional equations. Analytical inversion of the principal operator of one-dimensional systems in Sobolev spaces is considered. Theorems on the boundedness and bounded invertibility of the principal operator are proved. The inverse operator is represented by series and in closed form: the elements of the inverse matrix are integral or integro-differential operators.
MSC:
| 45K05 | Integro-partial differential equations |
| 45P05 | Integral operators |
| 45Q05 | Inverse problems for integral equations |
| 15A10 | Applications of generalized inverses |
| 78A45 | Diffraction, scattering |
Keywords:
diffraction; cylinder; operator matrix; Sobolev spaces; Lax-Milgram theorem; integral operator; singular operator; integro-differential operator; inverse matrixReferences:
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