On the weak formulation of the stochastic obstacle problems

On the weak formulation of the stochastic obstacle problems

Creators Ishikawa Masaaki

This paper is concerned with the weak formulation of stochastic obstacle problems. First, a mathematical model of a stochastic obstacle problem is given in a form of a variational inequality. The weak solution of the stochastic obstacle problem is defined. The relation between the weak solution and the strong one is stated. Secondly, under some conditions, it is proved that the weak solution exists by using the method of penalization. Finally, the existence of the maximum solution of the weak solution is shown. The mathematical formulation of stochastic obstacle problems by the strong solution is valid only for a one dimensional spatial variable, however, the weak solution proposed here enables to formulate the stochastic obstacle problems in a multi-dimensional spatial region.

[ISSN]0386-3433

[NCID]AA0086073X