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Anomalous Exponents In Nonlinear Diffusion

热1 yhhuang 添加于 2009-12-12 15:08 | 2271 次阅读 | 0 个评论

作者
Aronson DG, Vazquez JL
摘要
We present a technique to prove existence and analytic dependence with respect to the relevant perturbation parameters of the anomalous exponents appearing often in problems of continuum mechanics. Such exponents are related to the existence of suitable self-similar solutions. The basic ingredients of the technique are the existence of analytic families of curves, matching by means of the Implicit Function Theorem, and continuation in the relevant parameter. We demonstrate the method by investigating in full detail two quite different situations which involve diffusive phenomena and are formulated in terms of nonlinear parabolic equations: they are the source-type solutions of the Barenblatt equation of elasto-plastic filtration and the focusing solutions of the porous medium equation. The method is not limited to these two problems and has quite general scope. We describe several additional problems involving anomalous exponents where this technique can be applied, and we outline the ...
详细资料
- 文献种类: Journal Article
- 期刊名称: J. Nonlinear Sci
- 期卷页: 第72卷 348-351页
学科领域自然科学 » 数学
标签

asymptotics partial differential equations self-similar solutions
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