A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition

  • Mahmoud Mohammed Mostafa El-Borai Alexandria University
  • A. Tarek S.A. Alexandria University
Keywords: Stochastic partial differential equation, Pathwise uniqueness, Bihari’s inequality.

Abstract

In this paper, we shall discuss the uniqueness ”pathwise uniqueness” of the solutions of stochastic partial differential equations (SPDEs) with non-local initial condition,
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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.

Author Biographies

Mahmoud Mohammed Mostafa El-Borai, Alexandria University

Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

A. Tarek S.A., Alexandria University

Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt 

References

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Brent Oksendal, Stochastic Dierential Equations, Fifth Edition, Springer- Verlag.

T. YAMADA and S. WATANABE, On the uniqueness of solutions of stochastic dierential equations, J. Math. Kyoto Univ, 155-167, (1971) .

T. YAMADA and S.WATANABE,On the uniqueness of solutions of stochas- tic dierential equations II, J. Math. Kyoto Univ, 553-563, (1971) .

S. ALTAY and UWE SCHMACK, Lecture notes on the Yamada- Watan- abe Condition for the pathwise uniqueness of solutions of certain stochastic Dierential Equations, (2013).

Mahmoud M. El-Borai and Farouk K. Assaad,On the asymptotic Behavior of Some Nonlinear Parabolic Systems, KYUNGPOOK Math. J, 37-42, 37(1997).

Mahmoud M. El-Borai, On some fractional evolution equations with non- local conditions, International J. of pure and appl. Math. , vol 24, No. 3, 405-415, (2005).

Mahmoud M. El-Borai, On some stochastic fractional integro-dierential equations, Advanced in dynamical system and application, vol.1, No.1, 49-57, (2006).

Published
2019-01-31
How to Cite
El-Borai, M. M., & S.A., A. T. (2019). A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition. JOURNAL OF ADVANCES IN MATHEMATICS, 16, 8226-8233. https://doi.org/10.24297/jam.v16i0.8018
Section
Articles