On the uniqueness of linear convection--diffusion equations with integral boundary conditions

This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on unknown solutions. Generally, the uniqueness result of this...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Chiun-Chang, Lee, Mizuno, Masashi, Moon, Sang-Hyuck
Format: Article
Language:English
Subjects:
Boundary conditions
Convection
Dirichlet problem
Domains
Mathematical analysis
Uniqueness
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on unknown solutions. Generally, the uniqueness result of this type of equation is unclear. In this preliminary study, a uniqueness result is verified when the domain is sufficiently large or small. The main approach has an 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.
ISSN:2331-8422