國立清華大學 數學系

Abstract: We consider the semi-discrete semi-linear Ito stochastic heat equations [SHE] started at a non-random bounded initial profile. By a solution to SHE we mean a solution in mild form. We will first give local properties to solutions. When the underlying walk is sufficiently transient and the noise level is sufficiently low, the solution can be a.s. uniformly dissipative provided that the initial profile is summable. This is joint work with N. Georgiou, M. Joseph, D. Khoshnevisan and P. Mahboubi. Tea Time: 3:30PM, R707