On the uniqueness of linear convection–diffusion equations with integral boundary conditions
We investigate a class of convection–diffusion equations in an expanding domain involving a parameter, where we consider integral boundary conditions that depend non-locally on unknown solutions. Generally, the uniqueness result of this type of equation is unclear. In this work, we obtain a uniquene...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.396/ |
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| _version_ | 1825206311392903168 |
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| author | Lee, Chiun-Chang Mizuno, Masashi Moon, Sang-Hyuck |
| author_facet | Lee, Chiun-Chang Mizuno, Masashi Moon, Sang-Hyuck |
| author_sort | Lee, Chiun-Chang |
| collection | DOAJ |
| description | We investigate a class of convection–diffusion equations in an expanding domain involving a parameter, where we consider integral boundary conditions that depend non-locally on unknown solutions. Generally, the uniqueness result of this type of equation is unclear. In this work, we obtain a uniqueness result when the domain is sufficiently large or small. This approach has the advantage of transforming the integral boundary conditions into new Dirichlet boundary conditions so that we can obtain refined estimates, and the comparison theorem can be applied to the equations. Furthermore, we show a domain such that under different boundary data, the equation in this domain can have infinitely numerous solutions or no solution. This work may contribute to the first understanding of the domain size’s effect on the existence and uniqueness of the linear convection–diffusion equation with integral-type boundary conditions. |
| format | Article |
| id | doaj-art-7d02b4a6fb494d93b71f38c5a07c4622 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-7d02b4a6fb494d93b71f38c5a07c46222025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G119120610.5802/crmath.39610.5802/crmath.396On the uniqueness of linear convection–diffusion equations with integral boundary conditionsLee, Chiun-Chang0Mizuno, Masashi1Moon, Sang-Hyuck2Institute for Computational and Modeling Science, National Tsing Hua University, Hsinchu 30013, TaiwanDepartment of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-Ku, Tokyo, 101-8308, JapanDepartment of Mathematical Sciences, College of Natural Sciences, Ulsan National Institute of Science and Technology, Republic of KoreaWe investigate a class of convection–diffusion equations in an expanding domain involving a parameter, where we consider integral boundary conditions that depend non-locally on unknown solutions. Generally, the uniqueness result of this type of equation is unclear. In this work, we obtain a uniqueness result when the domain is sufficiently large or small. This approach has the advantage of transforming the integral boundary conditions into new Dirichlet boundary conditions so that we can obtain refined estimates, and the comparison theorem can be applied to the equations. Furthermore, we show a domain such that under different boundary data, the equation in this domain can have infinitely numerous solutions or no solution. This work may contribute to the first understanding of the domain size’s effect on the existence and uniqueness of the linear convection–diffusion equation with integral-type boundary conditions.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.396/ |
| spellingShingle | Lee, Chiun-Chang Mizuno, Masashi Moon, Sang-Hyuck On the uniqueness of linear convection–diffusion equations with integral boundary conditions Comptes Rendus. Mathématique |
| title | On the uniqueness of linear convection–diffusion equations with integral boundary conditions |
| title_full | On the uniqueness of linear convection–diffusion equations with integral boundary conditions |
| title_fullStr | On the uniqueness of linear convection–diffusion equations with integral boundary conditions |
| title_full_unstemmed | On the uniqueness of linear convection–diffusion equations with integral boundary conditions |
| title_short | On the uniqueness of linear convection–diffusion equations with integral boundary conditions |
| title_sort | on the uniqueness of linear convection diffusion equations with integral boundary conditions |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.396/ |
| work_keys_str_mv | AT leechiunchang ontheuniquenessoflinearconvectiondiffusionequationswithintegralboundaryconditions AT mizunomasashi ontheuniquenessoflinearconvectiondiffusionequationswithintegralboundaryconditions AT moonsanghyuck ontheuniquenessoflinearconvectiondiffusionequationswithintegralboundaryconditions |