| dc.description |
We endow the nonlinear degenerate parabolic equation used to describe propagation of thermal waves in plasma or in a porous medium, with a mechanism for flux saturation intended to correct the nonphysical gradient-flux relations at high gradients. We study both analytically and numerically the resulting equation: u<sub>t</sub>[u<sup>n</sup>Q(g(u)<sub>x</sub>)]<sub>x</sub>, n>0, where Q is a bounded increasing function. This model reveals that for n>1 the motion of the front is controlled by the saturation mechanism and instead of the typical infinite gradients resulting from the linear flux-gradients relations, Q∼u<sub>x</sub>, we obtain a sharp, shock-like front, typically associated with nonlinear hyperbolic phenomena. We prove that if the initial support is compact, independently of the smoothness of the initial datum inside the support, a sharp front discontinuity forms in a finite time, and until then the front does not expand. |
