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- W2119493548 abstract "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: ut = [unQ(g(u)x)]x, 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∼ux, 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." @default.
- W2119493548 created "2016-06-24" @default.
- W2119493548 creator A5045555983 @default.
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- W2119493548 date "2003-08-20" @default.
- W2119493548 modified "2023-09-29" @default.
- W2119493548 title "Formation of discontinuities in flux-saturated degenerate parabolic equations" @default.
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- W2119493548 doi "https://doi.org/10.1088/0951-7715/16/6/301" @default.
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