论文标题
关于线性对流的唯一性 - 具有整体边界条件的扩散方程
On the uniqueness of linear convection--diffusion equations with integral boundary conditions
论文作者
论文摘要
这项工作有助于理解域的大小对线性对流的存在和独特性的影响 - 扩散方程与积分型边界条件，其中边界条件非局部依赖于未知的解决方案。通常，这种类型的方程式的唯一性结果尚不清楚。在这项初步研究中，当域足够大或小时，可以验证唯一性结果。主要方法具有将积分边界条件转换为新的Dirichlet边界条件的一个优点，以便我们可以获得精致的估计，并且可以将比较定理应用于方程。此外，我们显示了一个域，因此在不同的边界数据下，该域中的方程可能具有无限的解决方案或没有解决方案。
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.
