论文标题
标量对流扩散方程的渐近行为
Asymptotic behavior of scalar convection-diffusion equations
论文作者
论文摘要
在这些讲义中，我们解决了以$ {r}^n $设置的标量对流扩散方程的解决方案的大渐近行为的问题。许多对流扩散方程的解决方案的大渐近行为与无穷大的初始数据的行为密切相关。实际上，当初始基准是可集成的并且是质量$ m $时，考虑到的方程式的解决方案通常会像质量$ m $的相关自相似概况一样，因此强调了缩放变量在这些情况下的作用。但是，这些方程还可以表现出其他渐近行为，包括弱的非线性，线性或强烈的非线性行为，具体取决于对流术语的形式。我们详尽地介绍了几种结果和技术，在其中清楚地区分了空间维度的作用和非线性对流术语的形式。 Borjan Geshovski的翻译（英语）
In these lecture notes, we address the problem of large-time asymptotic behaviour of the solutions to scalar convection-diffusion equations set in ${R}^N$. The large-time asymptotic behaviour of the solutions to many convection-diffusion equations is strongly linked with the behavior of the initial data at infinity. In fact, when the initial datum is integrable and of mass $M$, the solutions to the equations under consideration oftentimes behave like the associated self-similar profile of mass $M$, thus emphasising the role of scaling variables in these scenarios. However, these equations can also manifest other asymptotic behaviors, including weakly non-linear, linear or strongly non-linear behavior depending on the form of the convective term. We give an exhaustive presentation of several results and techniques, where we clearly distinguish the role of the spatial dimension and the form of the nonlinear convective term. Translation (English) by Borjan Geshovski
