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), [
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Figure 1. A sample path of an $\alpha$-stable Lévy subordinator $Z$ with ${\bf E} \text{e}^{-\lambda Z_1} = \text{e}^{-\lambda^\alpha}$ for $\alpha = 0.9$ (a); solutions $t\mapsto u_D(t, x)$ of equation (2.2) with Dirichlet boundary noise for $\nu = -1$, $x = 1$ (b) and $\nu = 1$, $x = 1$ (d); the concentration curve $x\mapsto u_D(t, x)$ for $\nu = 1$, $t = 55$ (c)
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