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Renormalization group calculation of anomalous exponents for nonlinear diffusion

热1 yhhuang 添加于 2010-4-16 11:43 | 1919 次阅读 | 0 个评论

作者
Caginalp G
摘要
We consider the heat equation with nonlinearity, u_t=u_xx+εf(x,u,u_x,u_xx), where ε is a small parameter. Using a renormalization group approach, we calculate that for large space and time, the solution is characterized by u(x,t)∼t^-1/2-αu^*(xt^-1/2,1), where α is a simple function of the powers of x, u, u_x, and u_xx in f. The same approach can be used to calculate the exponent and coefficient for finite time blow-up of equations such as u_t=u_xx+u^r, where r>1. In both cases the calculations can be performed within the standards of asymptotic analysis. © 1996 The American Physical Society.
详细资料
- 文献种类: Journal Article
- 期刊名称: Physical Review E
- 期刊缩写: Phys. Rev. E
- 期卷页: 1996年第53卷第1期 66-73页
- ISBN: 1063-651X
学科领域自然科学 » 数学
标签

renormalization group
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