APDE Seminar @UPV/EHU: Integrability of projective equatins and applications

Abstract

This talk consists of two parts. In the first part we consider integrability of a family of second-order differential equations that is a projection of a geodesic flow of a two-dimensional (pseudo) Riemannian manifold. We develop two approaches for establishing integrability of the projective equations. The first one is based on finding solution of equivalence problems for the family of projective equations and its integrable subcases. The second one is connected with the classification of quasi-polynomial invariants for the projective equations.

 In the second part of the talk we discuss a problem of mathematical modelling of wound healing in Drosophila embryos. We propose a mathematical model of this process, which is a system of nonlinear PDEs, demonstrate its correspondence to experimental data and discuss some properties of its solutions.