Exploring Solutions of Geometry Problems for Inverse Cauchy Problems in Helmholtz and Modified Helmholtz Equations
Abstract In the present paper explores a reverse Cauchy problem for a heat transfer issue described by the Helmholtz and modified Helmholtz equation. Our goal is to identify an unknown defect within a simply connected bounded domain , given the Dirichlet data (temperature) on the boundary , and...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
College of science, university of Diyala
2025-04-01
|
| Series: | Academic Science Journal |
| Subjects: | |
| Online Access: | https://acadscij.uodiyala.edu.iq/index.php/Home/article/view/312 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Abstract
In the present paper explores a reverse Cauchy problem for a heat transfer issue described by the Helmholtz and modified Helmholtz equation. Our goal is to identify an unknown defect within a simply connected bounded domain , given the Dirichlet data (temperature) on the boundary , and Neumann data (heat flux) on the boundary . We assume that the temperature satisfies the Helmholtz equation (or modified Helmholtz equation) that governs the heat condition in the fin. To solve this problem, we propose a method that involves two steps. First, we solve a Cauchy problem using the Helmholtz equation (or modified Helmholtz equation) to determine the temperature Then, in the second phase, we solve a system of nonlinear scalar equations to determine the coordinates of the points defining the boundary . This can be achieved using an iterative method, such as Newton's method.
|
|---|---|
| ISSN: | 2958-4612 2959-5568 |