Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint
We consider a two-dimensional parabolic problem subject to both Neumann and Dirichlet boundary conditions, along with an integral constraint. Based on the integral observation, we solve the inverse problem of a recovering time-dependent right-hand side. By exploiting the structure of the boundary co...
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MDPI AG
2025-06-01
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| Series: | Mathematics |
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| author | Miglena N. Koleva Lubin G. Vulkov |
| author_facet | Miglena N. Koleva Lubin G. Vulkov |
| author_sort | Miglena N. Koleva |
| collection | DOAJ |
| description | We consider a two-dimensional parabolic problem subject to both Neumann and Dirichlet boundary conditions, along with an integral constraint. Based on the integral observation, we solve the inverse problem of a recovering time-dependent right-hand side. By exploiting the structure of the boundary conditions, we reduce the original inverse problem to a one-dimensional formulation. We conduct a detailed analysis of the existence and uniqueness of the solution to the resulting one-dimensional loaded initial-boundary value problem. Furthermore, we derive estimates for both the solution and the unknown function. The direct and inverse problems are numerically solved by finite difference schemes. Numerical verification of the theoretical results is provided. |
| format | Article |
| id | doaj-art-56b9433bab3d4bc0a818d4ec307b0d0d |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-56b9433bab3d4bc0a818d4ec307b0d0d2025-08-20T02:32:57ZengMDPI AGMathematics2227-73902025-06-011311187610.3390/math13111876Source Identification for a Two-Dimensional Parabolic Equation with an Integral ConstraintMiglena N. Koleva0Lubin G. Vulkov1Department of Mathematics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, BulgariaDepartment of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, “Angel Kanchev” University of Ruse, 8 Studentska Str., 7017 Ruse, BulgariaWe consider a two-dimensional parabolic problem subject to both Neumann and Dirichlet boundary conditions, along with an integral constraint. Based on the integral observation, we solve the inverse problem of a recovering time-dependent right-hand side. By exploiting the structure of the boundary conditions, we reduce the original inverse problem to a one-dimensional formulation. We conduct a detailed analysis of the existence and uniqueness of the solution to the resulting one-dimensional loaded initial-boundary value problem. Furthermore, we derive estimates for both the solution and the unknown function. The direct and inverse problems are numerically solved by finite difference schemes. Numerical verification of the theoretical results is provided.https://www.mdpi.com/2227-7390/13/11/1876parabolic equationinverse problemsource identificationintegral measurementloaded equationexistence and uniqueness |
| spellingShingle | Miglena N. Koleva Lubin G. Vulkov Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint Mathematics parabolic equation inverse problem source identification integral measurement loaded equation existence and uniqueness |
| title | Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint |
| title_full | Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint |
| title_fullStr | Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint |
| title_full_unstemmed | Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint |
| title_short | Source Identification for a Two-Dimensional Parabolic Equation with an Integral Constraint |
| title_sort | source identification for a two dimensional parabolic equation with an integral constraint |
| topic | parabolic equation inverse problem source identification integral measurement loaded equation existence and uniqueness |
| url | https://www.mdpi.com/2227-7390/13/11/1876 |
| work_keys_str_mv | AT miglenankoleva sourceidentificationforatwodimensionalparabolicequationwithanintegralconstraint AT lubingvulkov sourceidentificationforatwodimensionalparabolicequationwithanintegralconstraint |