Theory and numerics for a semilinear elliptic pde, with an application in the theory of pseudoplastic fluids

Abstract

In this work we provide a survey of the existence, uniqueness, and analyticity of the solutions for the problem

We establish numerical solutions in one-and two-dimensional bounded regions using multigrid methods. Numerical examples are provided the demonstrate the necessity and/or sufficiency of some the conditions in the existence and uniquness theorems.

Keywords:

• Semilinear
• Elliptic
• Multigrid
• FAS
• Pseudoplastic flow

^∗This work was supported in part by the Naval Postgraduate School Research Council under grant No ZZ865-ZZ899/5986

^∗This work was supported in part by the Naval Postgraduate School Research Council under grant No ZZ865-ZZ899/5986

Notes

^∗This work was supported in part by the Naval Postgraduate School Research Council under grant No ZZ865-ZZ899/5986