Details of Research Outputs

In this paper we study the initial problem for a stochastic nonlinear equation arising from 1D integro-differential scalar conservation laws. The equation is driven by Lévy space-time white noise in the following form:(∂ - A) u + ∂ q (u) = f (u) + g (u) F for u : (t, x) ∈ (0, ∞) × R {mapping} u (t, x) ∈ R, where A is an integro-differential operator associated with a symmetric, nonlocal, regular Dirichlet form, and F stands for a Lévy space-time white noise. The problem is interpreted as a stochastic integral equation of jump type involving certain convolution kernels. Existence of a unique local (in time) L (R)-valued solution is obtained. © 2006 Elsevier Inc. All rights reserved.