Compactly supported solutions for a rimming flow model

We study a generally ill-posed Cauchy problem with 2π-periodic initial data for a nonlinear forward–backward heat equation. The problem is originated from a lubrication approximation of viscous rimming flow dynamics on the inner surface of a rotating horizontal cylinder in the presence of gravitational field. For a certain class of compactly supported initial data we prove local in time existence of generalized weak solutions. (paper)