具有快速对流的Heat equations：源型解和大时间行为
Heat equations with fast convection: source-type solutions and large-time behaviour
摘要：
在尾部控制假设下，研究了一类带快速对流项的热方程Cauchy问题源型解的存在唯一性。我们允许解改变符号，但实际上我们将证明它们与初始数据具有相同的符号，这是狄拉克δ的倍数。作为应用，我们获得了具有快速对流的热方程的具有可积初值的非负有界解的大时间行为，涵盖了自上世纪末以来一直开放的几个维度的情况。
英文摘要：
We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that they have the same sign as the initial data, which is a multiple of the Dirac delta. As an application, we obtain the large-time behaviour of nonnegative bounded solutions with integrable initial data to heat equations with fast convection, covering the case of several dimensions that remained open since the end of last century.
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