On a singularly perturbed system of two second-order equations in the case of intersecting roots of the degenerate equation

摘要

For a singularly perturbed system of two second-order differential equations (one rapid and one slow), we prove the existence of a solution and obtain its asymptotics for the case in which the degenerate equation has two intersecting roots. In addition, we show that this solution is an asymptotically stable stationary solution of the corresponding parabolic problem and find its local attraction domain. [PUBLICATION ABSTRACT]