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

点击翻译按钮获取中文摘要

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. ***