Mathematical Sciences: A Singular Semilinear Elliptic Boundary Value Problem in Fluid Theory

数学科学：流体理论中的奇异半线性椭圆边值问题

• 批准号: 9409253
• 负责人: Aihua Shaker
• 金额: $ 1.8万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9409253&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singular; Semilinear; Elliptic

940925 Shaker We study a singular semilinear elliptic boundary value problem in a bounded domain in the n dimensional real space. The importance of this problem in scientific applications has been widely recognized (see W ). The motivation for this proposal is three-fold. First we wish to generalize the existing theorems by relaxing the coefficient function in the equation from being Holder continuous to Lipschitz integrable. Second we are interested in possibilities of achieving similar results for systems of equations. A third impetus proceeds from our numerical results on the unit interval and unit square which have shown that multigrid methods can provide an efficient means of solution for reasonable choices of the coefficient function. However, an actual convergence proof for the multigrid Full Approximation Scheme (FAS) is very hard to obtain and the literature is remarkably sparse in the area of founding theory for the FAS method. Our future research into solution methods for the discussed problems will be to fill this gap and to investigate new and perhaps more efficient techniques such as the Multilevel Projection (PML) methods to deal with this type of nonlinear problems. ***

940925 Shaker我们研究了n维真实空间中有界域中的一个奇异的半线性椭圆边界值问题。该问题在科学应用中的重要性已得到广泛认可（请参阅W）。 该提议的动机是三倍。 首先，我们希望通过放宽方程式中的系数函数从连续到Lipschitz Entegnable中概括现有定理。其次，我们对方程式系统获得相似结果的可能性感兴趣。第三个动力从我们的数值结果和单位平方的数值结果中得出，这表明多格里德方法可以为合理选择系数函数提供有效的解决方案手段。 然而，很难获得多族全近似方案（FAS）的实际收敛证明，而文献在FAS方法的建立理论领域非常稀疏。我们对讨论问题的解决方案方法的未来研究将是填补这一空白，并研究新的，也许更有效的技术，例如多级投影（PML）方法来处理这种类型的非线性问题。 ***