Numerical computations to pulse splitting phenomena in the thermal waves through an absorbing medium

Nonlinear diffusion with strong absorption causes “total extinction in finite time” and “finite propagation of the initial support”. As the dynamical behavior of the support of pulses there is a possibility of the support to split, when the initial function has two local maxima. Thus pulse splitting phenomena appear. In this paper the difference scheme which predicts such phenomena is proposed. Moreover, the criterion for pulse non-splitting phenomena is also given. Several numerical experiments are presented.