Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics
Fully Nonlinear Equations with Applications to Grad Equations in Plasma Physics
复制标题
完全非线性方程及其在等离子体物理中梯度方程的应用
DOI：
10.1002/cpa.22026
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发表时间：
2023
影响因子：
3
通讯作者：
Tomasetti, Ignacio
中科院分区：
文献类型：
--
作者：
Caffarelli, Luis A.;Tomasetti, Ignacio
本文将Mossino和Temam在[7]中研究的一个方程推广到完全非线性的情形。该方程在等离子体物理学中作为格拉德方程的近似而出现，该方程由Harold格拉德在[4]中引入，用于模拟被限制在称为TOKAMAK的环形容器中的等离子体的行为。我们证明了粘性解的存在性和正则性（我们在边界附近改进了这种正则性）。这个问题的难点在于右侧，它涉及到超水平集的测度，使得问题非局部。© 2021 Wiley Periodicals LLC.
In this paper we generalize an equation studied by Mossino and Temam in [7], to the fully nonlinear case. This equation arises in plasma physics as an approximation to Grad equations, which were introduced by Harold Grad in [4], to model the behavior of plasma confined in a toroidal vessel called TOKAMAK. We prove existence of a ‐viscosity solution and regularity up to for any (we improve this regularity near the boundary). The difficulty of this problem lies in the right‐hand side which involves the measure of the superlevel sets, making the problem nonlocal. © 2021 Wiley Periodicals LLC.
DOI：
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发表时间：
2015
期刊：
影响因子：
--
作者：
H. Grad
通讯作者：
H. Grad