On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics
The paper is devoted to the theoretical analysis of the effects of boundary conditions on the solutions of the system of one-dimensional (1D) hemodynamics. The integral inequalities, which realize the energy inequalities for the solutions of initial-boundary-value problems, are obtained. It is demon...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/4058 |
| _version_ | 1797467383163518976 |
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| author | Gerasim V. Krivovichev |
| author_facet | Gerasim V. Krivovichev |
| author_sort | Gerasim V. Krivovichev |
| collection | DOAJ |
| description | The paper is devoted to the theoretical analysis of the effects of boundary conditions on the solutions of the system of one-dimensional (1D) hemodynamics. The integral inequalities, which realize the energy inequalities for the solutions of initial-boundary-value problems, are obtained. It is demonstrated that the unphysical unbounded solutions can take place for the case of bounded functions from boundary conditions. For the periodic boundary conditions, the integral estimation illustrates the correct behavior of the solution. For this case of boundary conditions, the effective Fourier method for the analytical solution is proposed. The analytical solutions, obtained by this approach, can be used for the comparison of different 1D blood-flow models. The results obtained in the paper allow for an the alternatively view of the stated boundary conditions and can explain some problems, which can arise in numerical simulations. They expand the possibilities of the application of analytical methods in the field of blood-flow simulation. The results can be useful for the specialists on blood-flow modeling. |
| first_indexed | 2024-03-09T18:51:52Z |
| format | Article |
| id | doaj.art-6446d48ee585471c8514f7eb38b7813c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:51:52Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6446d48ee585471c8514f7eb38b7813c2023-11-24T05:44:13ZengMDPI AGMathematics2227-73902022-11-011021405810.3390/math10214058On the Effects of Boundary Conditions in One-Dimensional Models of HemodynamicsGerasim V. Krivovichev0Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, 7/9 Universitetskaya Nab., 199034 Saint Petersburg, RussiaThe paper is devoted to the theoretical analysis of the effects of boundary conditions on the solutions of the system of one-dimensional (1D) hemodynamics. The integral inequalities, which realize the energy inequalities for the solutions of initial-boundary-value problems, are obtained. It is demonstrated that the unphysical unbounded solutions can take place for the case of bounded functions from boundary conditions. For the periodic boundary conditions, the integral estimation illustrates the correct behavior of the solution. For this case of boundary conditions, the effective Fourier method for the analytical solution is proposed. The analytical solutions, obtained by this approach, can be used for the comparison of different 1D blood-flow models. The results obtained in the paper allow for an the alternatively view of the stated boundary conditions and can explain some problems, which can arise in numerical simulations. They expand the possibilities of the application of analytical methods in the field of blood-flow simulation. The results can be useful for the specialists on blood-flow modeling.https://www.mdpi.com/2227-7390/10/21/4058blood flowone-dimensional modelboundary conditions |
| spellingShingle | Gerasim V. Krivovichev On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics Mathematics blood flow one-dimensional model boundary conditions |
| title | On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics |
| title_full | On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics |
| title_fullStr | On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics |
| title_full_unstemmed | On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics |
| title_short | On the Effects of Boundary Conditions in One-Dimensional Models of Hemodynamics |
| title_sort | on the effects of boundary conditions in one dimensional models of hemodynamics |
| topic | blood flow one-dimensional model boundary conditions |
| url | https://www.mdpi.com/2227-7390/10/21/4058 |
| work_keys_str_mv | AT gerasimvkrivovichev ontheeffectsofboundaryconditionsinonedimensionalmodelsofhemodynamics |