抄録
This paper is concerned with the mathematical formulation of stochastic parabolic systems with boundary conditions of subdifferential type. There are two methods to formulate systems with subdifferentials. One is by a strong solution, the other is a weak one. The formulation by the strong solution is effective only for a one-dimensional spatial region. Since the spatial region of the considered system is a multi-dimension, only the formulation by the weak solution is applicable to the considered system. In this paper, first, the system equation is given and the physical meaning of the subdifferential boundary condition is explained. The definitions of the weak and strong solutions are stated. And the relation between these two solutions is derived. Secondly, the existence theorem of the weak solution is given. Finally, it is shown that the weak solution has the maximum solution.
