摘要
研究了来源于石油开发中电阻率测井中的一类含薄层区域上的非线性退化椭圆型等值面边界值问题,在自由项与零阶项的系数均为L1可积的条件下,证明了问题有界弱解的存在性与唯一性。同时假定方程的系数满足一定收敛条件时,当薄层区域收敛于一曲面时,得到了问题解的极限性态。其结果表明,在实际计算中可以将原问题近似为一个没有薄层区域的交界面问题来处理。
This paper mainly study a class of boundary value problems with equivalued surface of nonlinear elliptic equations on a domain with thin layer arising in resistivity well-logging in petroleum exploitation.Under the assumptions that the coefficient of the zero order term and source term both belong to L1,the existence and uniqueness of bounded solutions to such problems are proved.Furthermore if the coefficients of the equation satisfy certain convergence conditions,the limit behaviour of solutions is studied as the thin layer converges to a surface.This result shows that in practical calculation,the boundary value problem with equivalued surface on the thin layer can be approximately replaced by the boundary value problem with equivalued interface.
作者
肖美萍
陈凌蕙
邹维林
XIAO Mei-ping;CHEN Ling-hui;ZOU Wei-lin(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)
出处
《南昌航空大学学报（自然科学版）》
CAS
2021年第1期22-27,共6页
Journal of Nanchang Hangkong University(Natural Sciences)
基金
国家自然科学基金(11461048,11801259)
江西省自然科学基金(20202BABL201009)
江西省教育厅科技项目(GJJ170604)。
关键词
退化椭圆方程
等值面边值问题
解的极限性态
degenerate elliptic equation
equivalued surface
limit behaviour of solutions
