Abstract
A Volterra equation on the infinite interval with a logarithmic kernel multiplied by a small parameter is analyzed. A Laplace transform solution is found; also, an approximate solution is given and proved to be uniformly asymptotic as the small parameter tends to zero for all time. The solution has an algebraic-logarithmic decay for large times. The Volterra equation is a model for the transport of charged particles in a random magnetic field.
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