PDE Seminar Abstracts

The Cauchy problem for a fourth-order thin film equation

Pablo Álvarez Caudevilla
Universidad Carlos III de Madrid, Spain
Mon 8 August 2011 2-3pm, Eastern Avenue Seminar Room 405


In this talk we will discuss different aspects of the Cauchy problem of a class of fourth order thin film equation of the form ut = Δ ((|u|nΔu). We will show recent results in which we obtained a countable number of similarity solutions of the thin film equation via a homotopy transformation as n 0+ to the similarity solutions of the classic bi-harmonic equation ut = Δ2u. Also, another similar homotopic approach is performed directly from the thin film equation to the parabolic bi-harmonic equation in order to obtain important properties for the Cauchy problem. This is a joint work with Prof. Victor. A. Galaktionov at the University of Bath (UK).