Advection-diffusion equation on a half-line with boundary Lévy noise
Lena-Susanne Hartmann, Ilya Pavlyukevich · Discrete and Continuous Dynamical Systems - B · 2018
In this paper we study a one-dimensional linear advection-diffusion equation on a half-line driven by a Lévy boundary noise. The problem is motivated by the study of contaminant transport models under random sources (P. P. Wang and C. Zheng, Ground water, 43 (2005), [ 34 ]). We determine the closed form formulae for mild solutions of this equation with Dirichlet and Neumann noise and study approximations of these solutions by classical solutions obtained with the help of Wong-Zakai approximations of the driving Lévy process.