S. N. Aristov, “Exact periodic and localized solutions of the equation <nobr>$h_t=\Delta\ln h$</nobr>”, Prikl. Mekh. Tekh. Fiz., 1999, Volume 40, Issue 1,Pages <nobr>22

This article is cited in 8 papers

Exact periodic and localized solutions of the equation $h_t=\Delta\ln h$

S. N. Aristov

Institute of Mechanics of Continua, Ural Division, Russian Academy of Sciences, Perm' 614013

Abstract: New exact regular solutions of the nonlinear-diffusion equation are found. Various types of evolution of certain classes of localized initial perturbations are described. We show that, when a localized distribution in the form of a ring is specified, the instantaneous occurrence of the singularity in its center results from the diffusive spreading.

UDC: 517.946

Received: 22.05.1997