Existence of solutions for electron balance problem in the stationary radio-frequency induction discharges

11th International Conference on "Mesh methods for boundary-value problems and applications"

Zheltukhin, V.S.^1 ; Solovyev, S.I.^2 ; Solovyev, P.S.^2 ; Chebakova, V.Yu.^2

Kazan State Technological University, 68 Karl Marx Street, Kazan

420015, Russia^1

Kazan Federal University, 18 Kremlevskaya Street, Kazan

420008, Russia^2

关键词: Eigenvalue problem;    Electron-balance;    Existence of Solutions;    Nonlinear dependence;    Radio frequencies;    Radio frequency discharges;    Reduced pressure;    Second-order ordinary differential equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012103/pdf
DOI  :  10.1088/1757-899X/158/1/012103

来源: IOP

【 摘 要 】

A sufficient condition for the existence of a minimal eigenvalue corresponding to a positive eigenfunction of an eigenvalue problem with nonlinear dependence on the parameter for a second order ordinary differential equation is established. The initial problem is approximated by the finite element method. Error estimates for the approximate minimal eigenvalue and corresponding positive eigenfunction are derived. Problems of this form arise in modelling the plasma of a radio-frequency discharge at reduced pressure.