The Cauchy problem for a fourth-order thin film equation

Pablo �lvarez Caudevilla
Universidad Carlos III de Madrid, Spain
Mon 8 August 2010 2-3pm, Eastern Avenue Seminar Room 405

Abstract

In this talk we will discuss different aspects of the Cauchy problem of a class of fourth order thin film equation of the form $u_t=\mathrm{\Delta }\cdot ((|u{|}^n\mathrm{\nabla }\mathrm{\Delta }u)$. 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 $n\to 0^{+}$ to the similarity solutions of the classic bi-harmonic equation $u_t={\mathrm{\Delta }}^{2}u$. 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 joint work with Prof. Victor. A. Galaktionov at the University of Bath (UK).

Check also the PDE Seminar page. Enquiries to Florica C�rstea or Daniel Daners.