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<p>This paper is devoted to exploring a new class of stochastic Benjamin-Bona-Mahony equation, which is a third-order nonlinear partial differential equation describing wave propagation. Initially, we established the solvability outcomes for the proposed systems by employing successive approximation techniques, Bihari inequality, stochastic concepts, and Grönwall’s inequality. Moreover, we derived the optimal control results for considered systems using the Marzur lemma and Balder’s theorem. Finally, we provide an example to illustrate the obtained results.</p>

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Successive approximation and optimal controls for stochastic Benjamin-Bona-Mahony equation

  • 期刊论文

  • 发表日期：

    2025年5月8日

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  • Rajesh Dhayal

摘要

This paper is devoted to exploring a new class of stochastic Benjamin-Bona-Mahony equation, which is a third-order nonlinear partial differential equation describing wave propagation. Initially, we established the solvability outcomes for the proposed systems by employing successive approximation techniques, Bihari inequality, stochastic concepts, and Grönwall’s inequality. Moreover, we derived the optimal control results for considered systems using the Marzur lemma and Balder’s theorem. Finally, we provide an example to illustrate the obtained results.