A Two Space Dimensional Semilinear Heat Equation Perturbed by White Noise

A two-space dimensional heat equation perturbed by a white noise driven in a bounded volume is considered. The equation is perturbed by a non-linearity of the type : f(AU) :, where : : means Wick (re)ordering with respect to the free solution; ; A are small parameters , U denotes a solution, f is the Fourier transform of a complex measure with compact support. Existence and uniqueness of the solution in a class of Colombeau-Oberguggenberger generalized functions is proven. An explicit construction of the solution is given and it is shown that each term of the expansion in a power series in is associated with an L 2-valued measure.