Justification of the exact asymptotics of the fundamental solution for a degenerate parabolic equation with a small parameter (Q6541668)

In this paper, the authors discuss the asymptotics of the fundamental solution of a linear degenerate parabolic equation with a small parameter. Using the operator representation of the Dirac delta function and the WKB method, they construct the asymptotic expansion with respect to the small parameter (i.e., the WKB expansion) of the fundamental solution for a class of linear degenerate parabolic equations. They also show that for this class of degenerate parabolic equations the WKB expansion of the fundamental solution converges, which immediately justifies the asymptotics of the WKB expansion.