In this talk, we will investigate the hitting properties of a class of stochastic partial differential equation (SPDEs). First, we consider the one-dimensional stochastic wave equation with a strictly positive initial position. We will show that with positive probability, the solution of this equation will hit zero in finite time.

Then, we add a u−α drift term, where α is a tuning parameter. We show that if α < 1, then again, there is a positive probability of the solution hitting zero in finite time; however, if α > 3, then with probability 1, the solution does not hit zero in finite time. Therefore, the critical α for the solution to not hit zero in finite time, if it exists, must lie between 1 and 3.