**Lecturer: **Aliona Dreglea

**Institute: **Irkutsk State University (Russia, Irkutsk)

**Date and time: **04.11.2013 - 11:00

**Details:**

In this talk the classification of the boundary value problems and models which appear in melt spinning process theory will be discussed. The existence theorem is proved demonstrating that there is a solution for two-points boundary value problem x (t) + R(x(t), t)x (t) = 0, α < t < β,
x(α) = a, x (α) = b, x(β) = c,
which arise in mathematical model of fiber spinning process. Similar problems appear in boundary layer theory. The boundary problem is reduced to the nonlinear integral equation using the Schauder fixed point theorem.
Robust numerical method employs the Shishkin meshes and applied for mathematical model of the melt spinning process.