论文标题
混合型抛物线方程的较高规律性理论
Higher Regularity Theory for a Mixed-Type Parabolic Equation
论文作者
论文摘要
在本文中，我们研究了混合型抛物线问题的较高规律性理论。我们将\ cite {dmr}的最新工作扩展到构建在Sobolev空间中具有任意数量的衍生物的解决方案。为了实现这一目标，我们介绍了一个基于称为“程度”数量的计数论点。在本文的第二部分中，我们将这种存在理论应用于古典Falkner-Skan自相似概况附近的PrandTL系统，以通过严格的构造论证来补充\ cite {im22}的稳定性分析。
In this paper, we study the higher regularity theory of a mixed-type parabolic problem. We extend the recent work of \cite{DMR} to construct solutions that have an arbitrary number of derivatives in Sobolev spaces. To achieve this, we introduce a counting argument based on a quantity called the "degree". In the second part of this paper, we apply this existence theory to the Prandtl system near the classical Falkner-Skan self-similar profiles in order to supplement the stability analysis of \cite{IM22} with a rigorous construction argument.
