RENORMALIZATION AND UNIVERSAL STRUCTURE OF BLOWUP IN 1D CONSERVATION LAWS

被引：0
|
作者：
Mailybaev, Alexei A. [1 ]
机构：
[1] Inst Nacl Matemat Pura & Aplicada IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, Brazil
来源：
HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS | 2014年 / 8卷
关键词：
Blowup; conservation law; universality; renormalization group; soliton; SINGULARITIES; EQUATIONS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss universality properties of blowup of 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. As a numerical example, blowup in ideal polytropic gas is considered.
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页码：783 / 789
页数：7
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