English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, the method of constructing the asymptotics of the fundamentalsolution of the Cauchy problem for a degenerate linear parabolic equation withsmall diffusion is considered. Based on the results obtained in \cite{dn}, thestudy extends them over the case of a degenerate equation. As in \cite{dn}, themain technique that allows us to switch from pseudo-differential equations topartial differential equations is the non-oscillating WKB method. A distinctivefeature of this work is a more detailed consideration on the characteristics ofthe Green's function in terms of symplectic geometry. The most significantintermediate result is presented as a theorem on the properties of thefundamental solution.

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