A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition
Keywords:Stochastic partial differential equation, Pathwise uniqueness, Bihari’s inequality.
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
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