Stochastic partial differential equations driven by Lévy space-time white noise (Q2722260)

This paper is mainly concerned with the parabolic stochastic partial differential equation (SPDE) NEWLINE\[NEWLINE\left(\frac{\partial}{\partial t}-\frac{\partial^{2}}{\partial x^{2}}\right)u(t,x)= a(t,x,u(t,x))+b(t,x,u(t,x))F_{t,x}NEWLINE\]NEWLINE on the given domain \([0,\infty)\times [0,L]\) with initial and Dirichlet boundary conditions, where \(F_{t,x}\) is the so-called Lévy space-time white noise consisting of the Gaussian space-time white noise (i.e., a Brownian sheet on \([0,\infty)\times [0,L])\) and the Poisson space-time white noise. Existence and uniqueness of the \(L^{2}\)-solution of the equation is presented so that for any initial value from \(L^{2}([0,L])\) a solution with càdlàg (i.e., right continuous with left hand limits) trajectories in \(L^{2}([0,L])\) is obtained. The flow property of the solution is discussed. The approach is based on combining the methods for solving SPDEs driven by the Gaussian noise with the technique for solving ordinary SDEs driven by the Lévy processes.