2 on the Solvability of Nonlinear Spdes

The Cauchy problem for 1-dimensional nonlinear sto-chastic partial diierential equations is studied. The uniqueness and existence of solutions in H 2 p (T)-space are proved. 1. Introduction The aim of this paper is to prove the unique solvability of the following one-dimensional nonlinear stochastic partial diierential equa-tions(SPDEs): du = a(t; x; u)u 00 + f(t; x)] dt + k (t)u 0 + g k (t; x)] dw k