A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition - El-Borai, Mahmoud Mohammed Mostafa; S.A., A. Tarek (JOURNAL OF ADVANCES IN MATHEMATICS, 2019)
In this paper, we shall discuss the uniqueness ”pathwise uniqueness” of the solutions of stochastic partial differential equations (SPDEs) with non-local initial condition, We shall use the Yamada-Watanabe condition for ”pathwise uniqueness” of the solutions of the stochastic differential equation; this condition is weaker than the usual Lipschitz condition. The proof is based on Bihari’s inequality.