三维静磁场Lipschitz区域上Robin问题广义解的存在与唯一性

Existence and Uniqueness for Generalized Solution of 3-D Magnetostatic Field Robin Problem in Lipschitz Domain

近年来 ,电磁场边值问题的数值解法取得了飞速的发展 .由于电磁场边值问题是一类非线性偏微分方程 ,研究解的存在性、唯一性具有较大的困难 .前人已讨论了 B- H间的几个基本不等式 ,并由之证明了三维静磁场带零边值问题广义解的存在与唯一性 ,作者也曾利用给出的 B- H间的不等式证明了三维静磁场 Neumann问题和二维时变场第一边值初值问题广义解的存在与唯一性 .由于在一般区域讨论存在困难 ,作者利用 Sobolev空间理论及单调算子理论证明了三维静磁场 L ipschitz区域上

During the past decades numerous calculations have achieved great development in magnetic field problems.There are special difficulties for the existence and uniqueness of the solutions for magnetic field problems because these problems are nonlinear partial differential eqations. For the first time, in [3] the authors discussed the inequalities of B-H and by using them the authors give a proof of the existence and uniqueness of the generalized solution for magnetostatic field problem with zero boundary value.By using the inequalities of B-H in[3],in[5,6] the authors give a proof of the existence and uniqueness of the generalized solutions for 3 D magnetostatic field Neumann problem and 2 D magnetic field first boundary value initial problem.Because of the difficulty for the discussion in general domain,the authors give a proof for the existence and uniqueness of the generalized solution for the 3 D magnetostatic field Robin problem in Lipschitz domain.