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.
Accepté le :
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Lee, Chiun-Chang 1 ; Mizuno, Masashi 2 ; Moon, Sang-Hyuck 3
CC-BY 4.0
@article{CRMATH_2023__361_G1_191_0,
author = {Lee, Chiun-Chang and Mizuno, Masashi and Moon, Sang-Hyuck},
title = {On the uniqueness of linear convection{\textendash}diffusion equations with integral boundary conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {191--206},
year = {2023},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
number = {G1},
doi = {10.5802/crmath.396},
language = {en},
url = {https://numdam.org/articles/10.5802/crmath.396/}
}
TY - JOUR AU - Lee, Chiun-Chang AU - Mizuno, Masashi AU - Moon, Sang-Hyuck TI - On the uniqueness of linear convection–diffusion equations with integral boundary conditions JO - Comptes Rendus. Mathématique PY - 2023 SP - 191 EP - 206 VL - 361 IS - G1 PB - Académie des sciences, Paris UR - https://numdam.org/articles/10.5802/crmath.396/ DO - 10.5802/crmath.396 LA - en ID - CRMATH_2023__361_G1_191_0 ER -
%0 Journal Article %A Lee, Chiun-Chang %A Mizuno, Masashi %A Moon, Sang-Hyuck %T On the uniqueness of linear convection–diffusion equations with integral boundary conditions %J Comptes Rendus. Mathématique %D 2023 %P 191-206 %V 361 %N G1 %I Académie des sciences, Paris %U https://numdam.org/articles/10.5802/crmath.396/ %R 10.5802/crmath.396 %G en %F CRMATH_2023__361_G1_191_0
Lee, Chiun-Chang; Mizuno, Masashi; Moon, Sang-Hyuck. On the uniqueness of linear convection–diffusion equations with integral boundary conditions. Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 191-206. doi: 10.5802/crmath.396
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