Editorial Board

JMI2011C-8 Numerically repeated support splitting and merging phenomena in a porous media equation with strong absorption (pp.61-68)

Author(s): Kenji Tomoeda

J. Math-for-Ind. 3C (2011) 61-68.

Nonlinear diffusion equations exhibit a wide variety of phenomena in the several fields of fluid dynamics, plasma physics and population dynamics. Among these the interaction between diffusion and absorption suggests a remarkable property in the behavior of the support of solution; that is, after support splitting phenomena appear, the support merges, and thereafter the support splits again. Moreover, numerically repeated support splitting and merging phenomena are observed. In this paper, making use of the properties of the particular solutions, we construct an initial function for which such phenomena appear.

Keyword(s).  nonlinear diffusion, support splitting, support merging, finite difference scheme