On the Fredholm Property and Solvability of a System of Integral Equations in the Transmission Problem for the Helmholtz Equation
A scalar three-dimensional boundary value problem of wave diffraction for the Helmholtz equation with transmission conditions that assume the presence of an infinitely thin material at the media interface is considered. Uniqueness and existence theorems for solutions are proved. The original problem...
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| Veröffentlicht in: | Differential equations 2023-08, Vol.59 (8), p.1095-1104 |
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| container_title | Differential equations |
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| creator | Smirnov, Yu. G. Kondyrev, O. V. |
| description | A scalar three-dimensional boundary value problem of wave diffraction for the Helmholtz equation with transmission conditions that assume the presence of an infinitely thin material at the media interface is considered. Uniqueness and existence theorems for solutions are proved. The original problem is reduced to a system of integral equations over the media interface. Calculation formulas for the system of linear algebraic equations obtained after applying the collocation method and numerical results for solving the problem when the domain is a ball with certain transmission conditions are given. |
| doi_str_mv | 10.1134/S0012266123080086 |
| format | Article |
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| ispartof | Differential equations, 2023-08, Vol.59 (8), p.1095-1104 |
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| language | eng |
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| subjects | Boundary value problems Collocation methods Difference and Functional Equations Electric waves Electromagnetic radiation Electromagnetic waves Electromagnetism Existence theorems Fredholm equations Helmholtz equations Integral Equations Linear algebra Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Uniqueness theorems Wave diffraction |
| title | On the Fredholm Property and Solvability of a System of Integral Equations in the Transmission Problem for the Helmholtz Equation |
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