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arXiv · 2009.07319

Asymptotics of Fundamental Solution of Cauchy Problem for Parabolic Equation with Small Parameter and Degeneration

Mark Rakhel
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Abstract

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.

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Mark Rakhel. 2020-09-15. Asymptotics of Fundamental Solution of Cauchy Problem for Parabolic Equation with Small Parameter and Degeneration. https://arxiv.org/abs/2009.07319

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