扩散方程的一般自相似解及相关构造
General self-similar solutions of diffusion equation and related constructions
摘要：
输运现象在科学技术中起着重要作用。在各种各样的应用中，平流和扩散都可能出现。关于扩散，在很长一段时间内，对于不同的非平衡系统，不同类型的衰减速率是可能的。在总结了正则扩散方程的现有解之后，我们给出了由三种不同的试探函数导出的不太为人所知的解，作为重点，我们给出了无限视界情形的一族解.通过这一点，我们试图向理解不同的扩散系统的不同的长时间衰减迈出一步。
英文摘要：
Transport phenomena plays an important role in science and technology. In the wide variety of applications both advection and diffusion may appear. Regarding diffusion, for long times, different type of decay rates are possible for different non-equilibrium systems. After summarizing the existing solutions of the regular diffusion equation, we present not so well known solution derived from three different trial functions, as a key point we present a family of solutions for the case of infinite horizon. By this we tried to make a step toward understanding the different long time decays for different diffusive systems.
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