论文标题
副参数和变性的抛物线方程的Cauchy问题基本解决方案的渐近解决方案的渐近学
Asymptotics of Fundamental Solution of Cauchy Problem for Parabolic Equation with Small Parameter and Degeneration
论文作者
论文摘要
在本文中，考虑了使用小扩散的退化线性抛物线方程来构建Cauchy问题基本解决方案的渐近解决方案的渐近方法。根据\ cite {dn}获得的结果，研究将它们扩展到退化方程式的情况下。如\ cite {dn}中一样，允许我们从伪差方程切换到部分微分方程的主要技术是非振荡的WKB方法。这项工作的一个独特特征是对绿色功能的特征在符号几何形状方面进行了更详细的考虑。最重要的中间结果作为基本解决方案特性的定理提出。
In this paper, the method of constructing the asymptotics of the fundamental solution of the Cauchy problem for a degenerate linear parabolic equation with small diffusion is considered. Based on the results obtained in \cite{dn}, the study extends them over the case of a degenerate equation. As in \cite{dn}, the main technique that allows us to switch from pseudo-differential equations to partial differential equations is the non-oscillating WKB method. A distinctive feature of this work is a more detailed consideration on the characteristics of the Green's function in terms of symplectic geometry. The most significant intermediate result is presented as a theorem on the properties of the fundamental solution.
