Theory and Numerics for a Semilinear Elliptic PDE with an Application in the Theory of Pseudoplastic Fluids 1996


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    • Author:  by Van Emden Henson  Aihua W. Shaker  

    • Abstract:  In this work we provide a survey of the existence, uniqueness, and analyticity of the solutions for the problem \Deltau + p(x)u \Gammafl = 0; x 2\Omega ` R n ; n 1: We establish numerical solutions in one- and two-dimensional bounded regions using multigrid methods. Numerical examples are provided that demonstrate the necessity and/or sufficiency of some the conditions in the existence and uniquness theorems. AMS Subject Classification: 35J25, 35J60, 65N55 Keywords: semilinear, elliptic, multigrid, FAS, pseudoplastic flow 1 Introduction We study the singular semilinear elliptic boundary value problem \Deltau + p(x)u \Gammafl = 0; x 2\Omega ` R n ; u j @\Omega = 0; (1) whose importance in scientific applications has been widely recognized [15]. In particular, in the case n = 1, the problem arises in the study of boundary layer equations for a class of non-Newtonian fluids, namely pseudoplastic fluids, under the classical conditions for a steady flow over a semi-infinite ...

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