The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation
Direct and inverse problems for a pseudoparabolic equation are considered. The direct (forward) problem is to find the solution of the corresponding initial–boundary-value problem for known model parameters, as well as the initial and boundary conditions. The well-posedness of the direct problem is...
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MDPI AG
2025-03-01
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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 | Direct and inverse problems for a pseudoparabolic equation are considered. The direct (forward) problem is to find the solution of the corresponding initial–boundary-value problem for known model parameters, as well as the initial and boundary conditions. The well-posedness of the direct problem is shown and a priori estimates of the solution are obtained. We study the inverse problem for identifying the flux on a part of the boundary of a rectangle, using integral measurement on the same part of the boundary. We first reduce the inverse problem to a direct one. The initial–boundary-value direct problem is with nonclassical (integrodifferential) boundary conditions. We develop a finite-difference scheme for numerically solving this problem. Numerical test examples demonstrate the effectiveness of the proposed method. It successfully handles the nonclassical integrodifferential boundary conditions and provides accurate numerical solutions. |
| format | Article |
| id | doaj-art-a004da4b606744a6963e14cb85700331 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-a004da4b606744a6963e14cb857003312025-08-20T02:42:22ZengMDPI AGMathematics2227-73902025-03-0113690810.3390/math13060908The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral ObservationMiglena 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, BulgariaDirect and inverse problems for a pseudoparabolic equation are considered. The direct (forward) problem is to find the solution of the corresponding initial–boundary-value problem for known model parameters, as well as the initial and boundary conditions. The well-posedness of the direct problem is shown and a priori estimates of the solution are obtained. We study the inverse problem for identifying the flux on a part of the boundary of a rectangle, using integral measurement on the same part of the boundary. We first reduce the inverse problem to a direct one. The initial–boundary-value direct problem is with nonclassical (integrodifferential) boundary conditions. We develop a finite-difference scheme for numerically solving this problem. Numerical test examples demonstrate the effectiveness of the proposed method. It successfully handles the nonclassical integrodifferential boundary conditions and provides accurate numerical solutions.https://www.mdpi.com/2227-7390/13/6/908pseudoparabolic equationinverse problemintegral observationpoint observationnonlocal boundary conditionsfinite-difference method |
| spellingShingle | Miglena N. Koleva Lubin G. Vulkov The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation Mathematics pseudoparabolic equation inverse problem integral observation point observation nonlocal boundary conditions finite-difference method |
| title | The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation |
| title_full | The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation |
| title_fullStr | The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation |
| title_full_unstemmed | The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation |
| title_short | The Numerical Solution of an Inverse Pseudoparabolic Problem with a Boundary Integral Observation |
| title_sort | numerical solution of an inverse pseudoparabolic problem with a boundary integral observation |
| topic | pseudoparabolic equation inverse problem integral observation point observation nonlocal boundary conditions finite-difference method |
| url | https://www.mdpi.com/2227-7390/13/6/908 |
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