The uniqueness and existence of solutions for the 3D Helmholtz equation in a step‐index waveguide with unbounded perturbation |
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| Authors: | Lihan Liu Yuehai Qin Yongzhi Xu Yuqiu Zhao |
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| Affiliation: | 1. Department of Mathematics, Sun Yat‐sen University, , Guangzhou, 510275 China;2. Department of Mathematics, Guangdong University of Education, , Guangzhou, 510303 China;3. Department of Mathematics, University of Louisville, , Louisville, KY, 40292 USA |
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| Abstract: | In this paper, we study the 3D Helmholtz equation in a step‐index waveguide with unbounded perturbation, allowing the presence of guided waves. Our assumptions on the perturbed and source terms are too few. On the basis of the Green's function for the 3D homogeneous Helmholtz equation in a step‐index waveguide without perturbation, we introduce a generalized (out‐going) Sommerfeld–Rellich radiation condition, and then we prove the uniqueness and existence of solutions for the studied 3D Helmholtz equation satisfying our radiation condition. Copyright © 2012 John Wiley & Sons, Ltd. |
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| Keywords: | Helmholtz equation step‐index waveguide unbounded perturbation existence of solutions uniqueness of solutions Green's function radiation condition |
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