The Boundary Value Problem for Elliptic Equation in the Corner Domain
- 作者: Perepelkin EE1, Polyakova RV1, Yudin IP1
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隶属关系:
- Joint Institute for Nuclear Research
- 期: 编号 2 (2014)
- 页面: 410-414
- 栏目: Articles
- URL: https://journals.rcsi.science/2658-4670/article/view/328541
- ID: 328541
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Modern accelerator systems and detectors contain magnetic systems of complex geometrical configuration. Design and optimization of the magnetic systems demand solving a nonlinear boundary-value problem of magnetostatic. The region in which the boundaryvalue problem is solved, consists of two sub-regions: a region of vacuum and a region of ferromagnetic. In view of the complex geometrical configuration of magnetic systems, the ferromagnetic/vacuum boundary can be nonsmooth, i.e. it contains a corner point near of which the boundary is formed by two smooth curves crossed in a corner point at some angle. For linear differential equations it is known that in such regions the solutions of the corresponding boundary-value problems can possess unlimitedly growing first derivatives near of the corner point. Some works consider a nonlinear differential equation of divergent type in the region with a corner and the opportunity of existence of solutions with unlimitedly growing module of gradient near the corner point is shown. The present work analyzes the region consisting of two sub-regions (ferromagnetic/vacuum) divided by a boundary with the corner point. In this region one considers a formulation of the magnetostatics problem with respect to two scalar potentials. Nonlinearity of the boundary-value problem is related to the function of magnetic permeability which depends upon the module of gradient of the solution to the boundary-value problem. In a case when the function of magnetic permeability at big fields satisfies certain conditions, in this work a theorem of limitation of the module of gradient of the solution near the corner point is proved.
作者简介
E Perepelkin
Joint Institute for Nuclear Research
Email: pevgeny@mail.ru
R Polyakova
Joint Institute for Nuclear Research
Email: polykovarv@mail.ru
I Yudin
Joint Institute for Nuclear Research
Email: yudin@jinr.ru
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