Universal structure of blow-up in 1D conservation laws

Details Universal structure of blow-up in 1D conservation laws Universal structure of blow-up in 1D conservation laws

2011-09-04

arxiv.org/abs/1109.0662v1

Physics

Mathematical Physics

8 pages, 2 figures

Scientific paper

We discuss universality properties of blow-up of a classical (smooth) solutions of conservation laws in one space dimension. It is shown that the renormalized wave profile tends to a universal function, which is independent both of initial conditions and of the form of a conservation law. This property is explained in terms of the renormalization group theory. A solitary wave appears in logarithmic coordinates of the Fourier space as a counterpart of this universality. Universality is demonstrated in two examples: Burgers equation and dynamics of ideal polytropic gas.

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