Exponential stability of the linear KdV-BBM equation
نویسندگان
چکیده
In this paper, we consider the following linear Korteweg–de Vries–Benjamin Bona Mahony (KdV-BBM) equation on a finite interval.$ \left\{ \begin{array}{ll} u_t - a^2u_{xxt} + u_x u_{xxx} = 0, & (x, t)\in(0, L)\times (0, \infty), \\ u(0, t) u(L, u_x(L, &t\in u(x, 0) u_0(x), x \in L). \end{array} \right. $We show well-posedness by semigroup theory. A set of critical length $ \mathcal{L} is obtained, for which system possesses conservative solutions. Then prove exponentially stability associated when L\not\in frequency domain method.
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems-series B
سال: 2023
ISSN: ['1531-3492', '1553-524X']
DOI: https://doi.org/10.3934/dcdsb.2023129