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Analyzing Approximate Solutions of the Cauchy Problem for Helmholtz Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 اردیبهشت 1405 اصل مقاله (1.13 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65700.3032 | ||
| نویسندگان | ||
| Davron Aslonqulovich Juraev1؛ Rakib Feyruz Efendiev2؛ Iqbol Ergashevich Niyozov3؛ Mohamed Abdalla* 4؛ Hala Abdelmaged5 | ||
| 1Scientific Research Center, Baku Engineering University, Baku AZ0102, Azerbaijan. | ||
| 2Department of Mathematics, Baku Engineering University, Baku AZ0102, Azerbaijan. | ||
| 3Department of Mathematical Physics and Functional Analysis, Samarkand State University named after Sharof Rashidov, Samarkand 140104, Uzbekistan. | ||
| 4Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia. | ||
| 5Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia. | ||
| چکیده | ||
| In this article, we address the challenge of recovering solutions to the Helmholtz equation within a confined three-dimensional space, utilizing information gathered from a section of the boundary. This scenario pertains to the Cauchy problem. By employing the Carleman function, we derive an explicit approximate solution. To tackle this problem, we leverage the Carleman function, a powerful tool in the study of partial differential equations. The Carleman estimate allows us to transition from boundary data to an approximate solution in the interior of the domain. | ||
| کلیدواژهها | ||
| Cauchy problem؛ Carleman function؛ regularized solution؛ ill-posed problems؛ conditionally posed problems | ||
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