Open AccessA Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition
Author(s) -
Mahmoud M. El-Borai
Publication year - 2019
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v16i0.8018
Subject(s) - mathematics , uniqueness , lipschitz continuity , stochastic partial differential equation , mathematical analysis , stochastic differential equation , initial value problem , partial differential equation
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’sinequality.