A construction of two different solutions to an elliptic system

Jacek Cyranka, Piotr Bogusław Mucha

Published 2015-02-11Version 1

The paper aims at constructing two different solutions to an elliptic system defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers 2D system. A motivation to consider the above system comes from an examination of unusual propetries of a linear operator. Roughly speaking a term effects in a special stabilization of the norms of the operator. We shall underline that the special features of this operator were found firstly via numerical analysis. Our proof is valid for a particular force, which is sufficiently large. The main steps of the proof concern finite dimension approximation of the system and concentrate on analysis of features of large matrices, which resembles standard numerical analysis.