论文标题
存在用于圆柱形langmuir探针的双种物种动力学模型的解决方案
Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe
论文作者
论文摘要
在本文中，我们研究了圆柱金属Langmuir探针附近的血浆无碰撞动力学模型。该模型由一个包含有规定边界条件的圆柱体之间的域中的Bi-Species Vlasov-Poisson方程组成。内部气缸对探针进行建模，而外部气缸与血浆芯的相互作用建模。我们证明了该模型的存在弱解决方案，因为我们为2 vlasov方程提供了一个弱的解决方案，并且是泊松方程的强大解决方案。本文的第一部分致力于解释该模型，并继续对Vlasov方程进行详细研究。这项研究导致对泊松方程的重新制定为一维非线性和非本地方程，我们证明它使用迭代的固定点可以接受强大的解决方案。
In this article, we study a collisionless kinetic model for plasmas in the neighborhood of a cylindrical metallic Langmuir probe. This model consists in a bi-species Vlasov-Poisson equation in a domain contained between two cylinders with prescribed boundary conditions. The interior cylinder models the probe while the exterior cylinder models the interaction with the plasma core. We prove the existence of a weak-strong solution for this model in the sense that we get a weak solution for the 2 Vlasov equations and a strong solution for the Poisson equation. The first parts of the article are devoted to explain the model and proceed to a detailed study of the Vlasov equations. This study leads to a reformulation of the Poisson equation as a 1D non-linear and non-local equation and we prove it admits a strong solution using an iterative fixed-point procedure.
