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<p>This paper explores the controllability of the generalized Benjamin–Bona–Mahony (BBM)-Burgers equation, incorporating a fourth-order dissipative term with hinged boundary condition. We begin by transforming the original equation into a coupled system composed of a second-order parabolic equation and an elliptic equation. Initially, we address the well-posedness of the linearized parabolic-elliptic system derived from the nonlinear problem. Subsequently, we prove the null controllability of this linear system through the application of Carleman’s inequality. Finally, utilizing the source terms method along with the Banach fixed-point theorem, we prove the local null controllability of the nonlinear parabolic-elliptic coupled system.</p>

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Local null-controllability of the generalized BBM-Burgers equation with a fourth-order dissipative term

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Mohmedmunavvar Mubarak Bapu

摘要

This paper explores the controllability of the generalized Benjamin–Bona–Mahony (BBM)-Burgers equation, incorporating a fourth-order dissipative term with hinged boundary condition. We begin by transforming the original equation into a coupled system composed of a second-order parabolic equation and an elliptic equation. Initially, we address the well-posedness of the linearized parabolic-elliptic system derived from the nonlinear problem. Subsequently, we prove the null controllability of this linear system through the application of Carleman’s inequality. Finally, utilizing the source terms method along with the Banach fixed-point theorem, we prove the local null controllability of the nonlinear parabolic-elliptic coupled system.