Properties of the Dirichlet Green's function for linear diffusions on a half line
Year: 2025
Type: article
Abstract: This article concerns the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian. Formulas for the Dirichlet Green's function on the half line are only known in special cases. The main object of study in the paper is the ratio of the Dirichlet to whole line Green's functions. Bounds, asymptotic behavior in the limit as the diffusion coefficient vanishes, and a log concavity result are obtained for this ratio. These results have been used in the proof of asymptotic behavior for a simple model of Ostwald ripening. For more information see https://ejde.math.txstate.edu/Volumes/2025/14/abstr.html
Authors: Joseph G. Conlon, Michael Dabkowski
Institutions: University of Michigan, University of Michigan–Dearborn
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407798520