Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation
In this paper, we suggest a method for recovering the unknown time-dependent strength of a contaminant concentration source from measurements of the concentration inside an unbounded domain. This problem is formulated as a Cauchy parabolic inverse problem. For its efficient numerical processing, the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/7/4536 |
| _version_ | 1827747074595094528 |
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| author | Slavi Georgiev Lubin Vulkov |
| author_facet | Slavi Georgiev Lubin Vulkov |
| author_sort | Slavi Georgiev |
| collection | DOAJ |
| description | In this paper, we suggest a method for recovering the unknown time-dependent strength of a contaminant concentration source from measurements of the concentration inside an unbounded domain. This problem is formulated as a Cauchy parabolic inverse problem. For its efficient numerical processing, the problem is solved by reduction of the Cauchy problem to a Dirichet one on a bounded domain using the method of the fundamental (potential) solutions in combination with an adjoint equation technique. A numerical solution to this approach is explained. Next, by choosing the source strength in the form of a finite series of shape functions with unknown constant coefficients and using a linear-square method, the term concentration source is estimated. Computational simulations using model examples from water pollution are discussed. |
| first_indexed | 2024-03-11T05:42:02Z |
| format | Article |
| id | doaj.art-8dbb6b2426a341a8b26bebe24332b306 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T05:42:02Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-8dbb6b2426a341a8b26bebe24332b3062023-11-17T16:21:45ZengMDPI AGApplied Sciences2076-34172023-04-01137453610.3390/app13074536Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion EquationSlavi Georgiev0Lubin Vulkov1Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaDepartment of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, BulgariaIn this paper, we suggest a method for recovering the unknown time-dependent strength of a contaminant concentration source from measurements of the concentration inside an unbounded domain. This problem is formulated as a Cauchy parabolic inverse problem. For its efficient numerical processing, the problem is solved by reduction of the Cauchy problem to a Dirichet one on a bounded domain using the method of the fundamental (potential) solutions in combination with an adjoint equation technique. A numerical solution to this approach is explained. Next, by choosing the source strength in the form of a finite series of shape functions with unknown constant coefficients and using a linear-square method, the term concentration source is estimated. Computational simulations using model examples from water pollution are discussed.https://www.mdpi.com/2076-3417/13/7/4536parabolic Cauchy problemboundary conditionsdispersion modelingpoint sourceinverse problemadjoint equation |
| spellingShingle | Slavi Georgiev Lubin Vulkov Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation Applied Sciences parabolic Cauchy problem boundary conditions dispersion modeling point source inverse problem adjoint equation |
| title | Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation |
| title_full | Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation |
| title_fullStr | Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation |
| title_full_unstemmed | Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation |
| title_short | Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation |
| title_sort | determination of a time varying point source in cauchy problems for the convection diffusion equation |
| topic | parabolic Cauchy problem boundary conditions dispersion modeling point source inverse problem adjoint equation |
| url | https://www.mdpi.com/2076-3417/13/7/4536 |
| work_keys_str_mv | AT slavigeorgiev determinationofatimevaryingpointsourceincauchyproblemsfortheconvectiondiffusionequation AT lubinvulkov determinationofatimevaryingpointsourceincauchyproblemsfortheconvectiondiffusionequation |